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myref.bib
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@article{Eymard2010,
author = {Eymard, R. and Gallou{\"{e}}t, T. and Herbin, R.},
journal = {IMA Journal of Numerical Analysis},
keywords = {finite-volume schemes,heterogeneous anisotropic diffusion,nonconforming grids},
number = {4},
pages = {1009--1043},
title = {{Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes}},
volume = {30},
year = {2010}
}
@article{renard2009,
title={A new fictitious domain approach inspired by the extended finite element method},
author={Haslinger, Jaroslav and Renard, Yves},
journal={SIAM Journal on Numerical Analysis},
volume={47},
number={2},
pages={1474--1499},
year={2009},
publisher={SIAM}
}
@article{cumsille2014,
title={A novel model for biofilm growth and its resolution by using the hybrid immersed interface-level set method},
author={Cumsille, Patricio and Asenjo, Juan A and Conca, Carlos},
journal={Computers \& Mathematics with Applications},
volume={67},
number={1},
pages={34--51},
year={2014},
publisher={Elsevier}
}
@article{zhang2017,
title={Modeling of Biofilm Growth on Ager Substrate Using the Extended Finite Element Method},
author={Zhang, Xianlong and Wang, Xiaoling and Sun, Qingping},
journal={Procedia IUTAM},
volume={23},
pages={33--41},
year={2017},
publisher={Elsevier}
}
@article{renard2016,
title={A fictitious domain method for frictionless contact problems in elasticity using Nitsche's method},
author={Fabre, Mathieu and Pousin, J{\'e}r{\^o}me and Renard, Yves},
journal={SMAI Journal of Computational Mathematics},
volume={2},
pages={19--50},
year={2016}
}
@article{barbosa1991,
title={The finite element method with Lagrange multipliers on the boundary: circumventing the Babu{\v{s}}ka-Brezzi condition},
author={Barbosa, Helio JC and Hughes, Thomas JR},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={85},
number={1},
pages={109--128},
year={1991},
publisher={Elsevier}
}
@article{Frey2012,
title={Computation of the signed distance function to a discrete contour on adapted triangulation},
author={Dapogny, Charles and Frey, Pascal},
journal={Calcolo},
volume={49},
number={3},
pages={193--219},
year={2012},
publisher={Springer}
}
@book{quarteroni1994,
title={Numerical Approximation of Partial Differential Equations},
author={Quarteroni, Alfio and Valli, Alberto},
year={1994},
publisher={Springer}
}
@book{osher2006book,
title={Level set methods and dynamic implicit surfaces},
author={Osher, Stanley and Fedkiw, Ronald},
volume={153},
year={2006},
publisher={Springer Science \& Business Media}
}
@article{chen1995,
title={Lattice methods and their applications to reacting systems},
author={Chen, Shiyi and Dawson, SP and Doolen, GD and Janecky, DR and Lawniczak, A},
journal={Computers \& chemical engineering},
volume={19},
number={6-7},
pages={617--646},
year={1995},
publisher={Elsevier}
}
@article{Eymard2008,
title={Discretization schemes for heterogeneous and anisotropic diffusion problems on general nonconforming meshes},
author={Eymard, Robert and Gallou{\"e}t, Thierry and Herbin, Raphaele},
journal={Available online as HAL report},
volume={203269},
year={2008}
}
@article{DiPietro2010,
author = {{Di Pietro}, Daniele A. and Ern, Alexandre},
doi = {10.1090/S0025-5718-10-02333-1},
issn = {0025-5718},
journal = {Mathematics of Computation},
number = {271},
pages = {1303--1330},
title = {{Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations}},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-77956573267{\&}partnerID=tZOtx3y1},
volume = {79},
year = {2010}
}
@book{Ainsworth1997,
author = {Ainsworth, Mark and Oden, J.Tinsley T},
booktitle = {Computer Methods in Applied Mechanics and Engineering},
doi = {10.1016/S0045-7825(96)01107-3},
editor = {{Myron B. Allen III, David A. Cox}, Peter Lax},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/uniqueness existence nonlinear system/a posteriori error fem - Mark Ainsworth - Tinsley Oden BOOK.pdf:pdf},
isbn = {047129411X},
issn = {00457825},
publisher = {John Wiley and Sons},
title = {{A posteriori error estimation in finite element analysis}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045782596011073},
year = {1997}
}
@book{Debnath2005,
author = {Debnath, L and Mikusi{\'{n}}ski, P},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/back{\_}ground/analysis/hilbert spaces with applications - Debnath - Mikusinski.pdf:pdf},
isbn = {9780122084386},
title = {{Hilbert spaces with applications}},
year = {2005}
}
@book{Leoni2009,
author = {Leoni, Giovanni},
file = {:Users/dinhanhthi/Library/Application Support/Mendeley Desktop/Downloaded/Leoni - 2009 - A first course in Sobolev spaces.pdf:pdf},
isbn = {9780821847688},
mendeley-groups = {background},
publisher = {American Mathematical Society},
title = {{A first course in Sobolev spaces}},
volume = {105},
year = {2009}
}
@article{Baratchart2016,
archivePrefix = {arXiv},
arxivId = {arXiv:1412.3283v1},
author = {Baratchart, Laurent and Bourgeois, Laurent and Leblond, Juliette},
doi = {10.1016/j.jfa.2016.01.011},
eprint = {arXiv:1412.3283v1},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/back{\_}ground/analysis/robin laplace exist unique.pdf:pdf},
issn = {10960783},
journal = {Journal of Functional Analysis},
keywords = {Elliptic regularity,Holomorphic Hardy-Smirnov classes,Robin inverse problem,Unique continuation},
number = {7},
pages = {2508--2542},
title = {{Uniqueness results for inverse Robin problems with bounded coefficient}},
volume = {270},
year = {2016}
}
@article{Duddu2006,
author = {Duddu, Ravindra and Bordas, S and Moran, Brian and Chopp, David L},
journal = {International journal for numerical method in engineering int.},
keywords = {Biofilm,Level set,Velocity extension,XFEM},
language = {english},
number = {847},
pages = {1--33},
title = {{A combined extended finite element and level set method for biofilm growth}},
volume = {2},
year = {2006}
}
@book{Rittmann2001,
author = {Rittmann, Bruce E. and McCarty, Perry L.},
file = {:C$\backslash$:/Users/dinha/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/B.E, McCarty - 2001 - Environmental Biotechnology.pdf:pdf},
isbn = {0-07-118184-9},
mendeley-groups = {level set method},
publisher = {Mc Graw Hill},
title = {{Environmental Biotechnology: principles and applications}},
year = {2001}
}
@book{Walker2008,
author = {Walker, V. K. and Wilson, S. L. and Wu, Z. and Miao, D. N. and Zeng, H. and Ripmeester, J. A. and Palmer, G. R.},
booktitle = {Emerging Environmental Technologies},
doi = {10.1007/978-1-4020-8786-8},
file = {:C$\backslash$:/Users/dinha/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Walker et al. - 2008 - Emerging Environmental Technologies.pdf:pdf},
isbn = {978-1-4020-8785-1},
keywords = {Gas hydrates,antifreeze proteins,freeze-thaw,gas exploration,ice affinity,ice nucleators,overwintering},
pages = {29--41},
title = {{Emerging Environmental Technologies}},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-68149172274{\&}partnerID=tZOtx3y1},
year = {2008}
}
@article{Duddu2008,
author = {Duddu, Ravindra and Chopp, David L and Moran, Brian},
doi = {10.1002/bit.22233},
institution = {Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208, USA. r-duddu@northwestern.edu},
issn = {1097-0290},
journaltitle = {Biotechnology and bioengineering},
month = may,
number = {1},
pages = {92--104},
pmid = {19213021},
title = {{A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment.}},
volume = {103},
year = {2008}
}
@article{Mah2001,
author = {Mah, Thien-Fah C. and O'Toole, George A.},
issn = {0966-842X},
journal = {Trends in microbiology},
month = jan,
number = {1},
pages = {34--9},
pmid = {11166241},
title = {{Mechanisms of biofilm resistance to antimicrobial agents}},
volume = {9},
year = {2001}
}
@article{Chopp2002,
author = {Chopp, David L and Kirisits, M J and Moran, Brian and Parsek, M R},
doi = {10.1038/sj.jim.7000316},
issn = {1367-5435},
journal = {Journal of industrial microbiology \& biotechnology},
mendeley-groups = {biofilm,papers},
month = dec,
number = {6},
pages = {339--46},
pmid = {12483476},
title = {{A mathematical model of quorum sensing in a growing bacterial biofilm.}},
volume = {29},
year = {2002}
}
@book{Thomee2006,
author = {Thom\'{e}e, Vidar},
edition = {2},
editor = {Bank, R. and Graham, R.L. and Stoer, J. and Varga, R. and Yserentant, H.},
isbn = {978-3-540-33122-3},
keywords = {Galerkin methods,differential equations,finite element theory,parabolic partial},
pages = {370},
publisher = {Springer},
series = {Springer Series in Computational Mathematics},
title = {{Galerkin Finite Element Methods for Parabolic Problems}},
volume = {25},
year = {2006}
}
@book{Knabner2002,
address = {New York},
author = {Knabner, Peter and Angermann, Lutz},
editor = {Marsden, J.E. and Sirovich, L. and Antman, S.S.},
isbn = {038795449X},
keywords = {numerical method},
pages = {442},
publisher = {Springer},
series = {Texts in Applied Mathematics},
title = {{Numerical Methods for Elliptic and Parabolic Partial Differential Equations}},
year = {2002}
}
@article{Picioreanu2000,
author = {Picioreanu, Cristian and {Van Loosdrecht}, M C and Heijnen, J J},
issn = {0006-3592},
journal = {Biotechnology and bioengineering},
keywords = {Algorithms,Biofilms,Biological,Biotechnology,Biotechnology: methods,Diffusion,Models,Surface Properties},
month = sep,
number = {5},
pages = {504--15},
pmid = {10898860},
title = {{Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study.}},
volume = {69},
year = {2000}
}
@book{picioreanuThesis,
title={Multidimensional modeling of biofilm structure},
author={Picioreanu, Cristian and van Loosdrecht, M and Heijnen, J},
year={1999},
publisher={Delft University of Technology, Faculty of Applied Sciences}
}
@article{Rittma1982,
author = {Rittman, B E},
doi = {10.1002/bit.260240219},
issn = {0006-3592},
journal = {Biotechnology and bioengineering},
number = {2},
pages = {501--506},
pmid = {18546318},
title = {{The Effect of Shear Stress on Bioflm Loss Rate}},
volume = {24},
year = {1982}
}
@article{monod1949,
author = { Jacques Monod },
title = {The Growth of Bacterial Cultures},
journal = {Annual Review of Microbiology},
volume = {3},
number = {1},
pages = {371-394},
year = {1949},
doi = {10.1146/annurev.mi.03.100149.002103}
}
@article{picioreanu2001,
title={Two-dimensional model of biofilm detachment caused by internal stress from liquid flow},
author={Picioreanu, Cristian and Van Loosdrecht, Mark CM and Heijnen, Joseph J and others},
journal={Biotechnology \& Bioengineering},
volume={72},
number={2},
pages={205--218},
year={2001},
publisher={Citeseer}
}
@article{cogan2007,
title={Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics},
author={Cogan, NG},
journal={Journal of theoretical biology},
volume={248},
number={2},
pages={340--349},
year={2007},
publisher={Elsevier}
}
@article{cogan2008,
title={Two-fluid model of biofilm disinfection},
author={Cogan, NG},
journal={Bulletin of mathematical biology},
volume={70},
number={3},
pages={800--819},
year={2008},
publisher={Springer}
}
@article{Cogan2006,
author = {Cogan, N G},
doi = {10.1016/j.jtbi.2005.06.017},
issn = {0022-5193},
journal = {Journal of theoretical biology},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Bacteria,Bacteria: cytology,Bacterial Infections,Bacterial Infections: transmission,Bacterial Physiological Phenomena,Biofilms,Dose-Response Relationship, Drug,Drug Resistance,Models, Biological},
month = feb,
number = {3},
pages = {694--703},
pmid = {16125727},
title = {{Effects of persister formation on bacterial response to dosing.}},
volume = {238},
year = {2006}
}
@article{Cogan2005,
author = {Cogan, N G and Cortez, Ricardo and Fauci, Lisa},
doi = {10.1016/j.bulm.2004.11.001},
issn = {0092-8240},
journal = {Bulletin of mathematical biology},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Biofilms,Biofilms: growth \& development,Computer Simulation,Drug Resistance, Bacterial,Hypochlorous Acid,Hypochlorous Acid: pharmacology,Models, Biological,Pseudomonas aeruginosa,Pseudomonas aeruginosa: growth \& development,Rheology},
month = jul,
number = {4},
pages = {831--53},
pmid = {15893555},
title = {{Modeling physiological resistance in bacterial biofilms.}},
volume = {67},
year = {2005}
}
@article{Picioreanu1999,
author = {Picioreanu, Cristian and Loosdrecht, Van and {M Cheijnen}, J J},
doi = {10.1016/S0273-1223(99)00158-4},
issn = {02731223},
journal = {Water Science and Technology},
keywords = {biofilm,convection,diffusion,flow,multidimensional modelling,porosity,roughness,structure},
number = {7},
pages = {115--122},
publisher = {International Asssociation on Water Quality},
title = {{Discrete-differential modelling of biofilm structure}},
volume = {39},
year = {1999}
}
@article{murga1995,
title={Quantitative analysis of biofilm thickness variability},
author={Murga, Ricardo and Stewart, Philip S and Daly, Don},
journal={Biotechnology and bioengineering},
volume={45},
number={6},
pages={503--510},
year={1995},
publisher={Wiley Online Library}
}
@article{Chopp2007,
year={2007},
isbn={978-0-387-31201-9},
booktitle={Deformable Models},
series={Topics in Biomedical Engineering. International Book Series},
doi={10.1007/978-0-387-68413-0_1},
title={Simulating Bacterial Biofilms},
url={http://dx.doi.org/10.1007/978-0-387-68413-0_1},
publisher={Springer New York},
author={Chopp, DavidL.},
pages={1-31}
}
@article{Roberts2005,
author = {Roberts, Mark E and Stewart, Philip S},
doi = {10.1099/mic.0.27385-0},
issn = {1350-0872},
journal = {Microbiology (Reading, England)},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Bacteria,Bacteria: cytology,Bacteria: drug effects,Bacteria: growth \& development,Bacterial,Biofilms,Biofilms: drug effects,Biofilms: growth \& development,Biological,Culture Media,Drug Resistance,Microbial Sensitivity Tests,Models,Plankton,Plankton: drug effects,Plankton: growth \& development},
month = jan,
number = {Pt 1},
pages = {75--80},
pmid = {15632427},
title = {{Modelling protection from antimicrobial agents in biofilms through the formation of persister cells.}},
volume = {151},
year = {2005}
}
@article{Davies2003,
author = {Davies, David},
doi = {10.1038/nrd1008},
issn = {1474-1776},
journal = {Nature reviews. Drug discovery},
keywords = {Animals,Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacokinetics,Anti-Bacterial Agents: pharmacology,Bacterial Infections,Bacterial Infections: microbiology,Bacterial Infections: pathology,Bacterial Physiological Phenomena,Biofilms,Biofilms: drug effects,Drug Resistance, Bacterial,Humans},
month = feb,
number = {2},
pages = {114--22},
pmid = {12563302},
title = {{Understanding biofilm resistance to antibacterial agents.}},
volume = {2},
year = {2003}
}
@article{Korotov2009,
author = {Kar{\'{a}}tson, J{\'{a}}nos and Korotov, Sergey},
file = {:C$\backslash$:/Dropbox/PhD/docs/fem{\_}methods/nonlinear - fixed - iterative - newton/discrete max principle fem elliptic interface - korotov 2009.pdf:pdf},
isbn = {978-951-22-8445-0},
issn = {17055105},
journal = {International Journal of Numerical Analysis and Modeling},
keywords = {Discrete maximum principle,Finite element method,Interface problem,Maximum principle,Nonlinear elliptic problem,Simplicial mesh},
number = {1},
pages = {1--16},
title = {{Discrete maximum principles for FEM solutions of some nonlinear elliptic interface problems}},
volume = {6},
year = {2009}
}
@article{Zenisek1987,
author = {Feistauer, Miloslav and {\v{Z}}en{\'{i}}{\v{s}}ek, Alexander},
doi = {10.1007/BF01396664},
file = {:C$\backslash$:/Dropbox/PhD/docs/fem{\_}methods/nonlinear - fixed - iterative - newton/fem sol nonlinear elliptic - zenisek 1987.pdf:pdf},
issn = {0029-599X},
journal = {Numer. Math.},
number = {4},
pages = {451--475},
title = {{Finite element solution of nonlinear elliptic problems}},
url = {http://dx.doi.org/10.1007/BF01396664},
volume = {50},
year = {1987}
}
@article{Chen2011,
title={Existence of positive solutions for semilinear elliptic systems with indefinite weight},
author={Chen, Ruipeng},
journal={Electronic Journal of Differential Equations},
volume={2011},
number={164},
pages={1--8},
year={2011}
}
@article{Chen1998,
author = {Chen, Zhiming and Zou, Jun},
journal = {Numerische Mathematik},
pages = {1--23},
title = {{Finite element methods and their convergence for elliptic and parabolic interface problems}},
url = {http://link.springer.com/article/10.1007/s002110050336},
year = {1998}
}
@article{Bramble1996,
author = {Bramble, JH and King, JT},
journal = {Advances in Computational Mathematics},
keywords = {finite element method,interface problems},
pages = {33},
title = {{A finite element method for interface problems in domains with smooth boundaries and interfaces}},
url = {http://link.springer.com/article/10.1007/BF02127700},
volume = {05},
year = {1996}
}
@article{Babuska1970,
author = {Babuska, I},
journal = {Computing},
pages = {207--213},
title = {{The finite element method for elliptic equations with discontinuous coefficients}},
url = {http://link.springer.com/article/10.1007/BF02248021},
volume = {218},
year = {1970}
}
@article{Ladyzhenskaya1966,
author = {Ladyzhenskaya, O.A.},
journal = {Trudy Mat. Inst. Steklov},
pages = {116--146},
title = {{The solvability of diffraction problems}},
volume = {92},
year = {1966}
}
@article{Li2003,
author = {Li, Zhilin and Lin, Tao and Wu, Xiaohui},
doi = {10.1007/s00211-003-0473-x},
issn = {0029-599X},
journal = {Numerische Mathematik},
month = nov,
number = {1},
pages = {61--98},
title = {{New Cartesian grid methods for interface problems using the finite element formulation}},
url = {http://link.springer.com/10.1007/s00211-003-0473-x},
volume = {96},
year = {2003}
}
@article{Sinha,
author = {Sinha, Rajen Kumar and Deka, Bhupen},
issn = {1464-3642},
journal = {IMA journal of numerical analysis},
keywords = {an unfitted finite-element method,elliptic and parabolic interface problems,error estimates,spatially discrete and fully discrete schemes},
language = {eng},
number = {3},
pages = {529--549},
publisher = {Oxford University Press},
title = {{An unfitted finite-element method for elliptic and parabolic interface problems}},
url = {http://cat.inist.fr/?aModele=afficheN\&cpsidt=21601006},
volume = {27},
year = {2005}
}
@article{Wu,
archivePrefix = {arXiv},
arxivId = {arXiv:1007.2893v1},
author = {Wu, Haijun and Xiao, Yuanming},
eprint = {arXiv:1007.2893v1},
keywords = {elliptic interface problems,hp -ipfem,unfitted mesh},
pages = {1--23},
title = {{An unfitted hp -interface penalty finite element method for elliptic interface problems}},
year = {2010}
}
@article{Hansbo2002,
author = {Hansbo, Anita and Hansbo, Peter},
journal={Computer methods in applied mechanics and engineering},
mendeley-groups = {interface,fem},
pages = {5537--5552},
title = {{An unfitted finite element method, based on Nitsche's method, for elliptic interface problems}},
url = {http://www.sciencedirect.com/science/article/pii/S0045782502005248},
volume = {191},
year = {2002}
}
@article{Barrau2012,
author = {Barrau, Nelly and Becker, Roland and Dubach, Eric and Luce, Robert},
doi = {10.1016/j.crma.2012.09.018},
issn = {1631073X},
journal = {Comptes Rendus Mathematique},
month = aug,
number = {15-16},
pages = {789--792},
publisher = {Elsevier Masson SAS},
title = {{A robust variant of NXFEM for the interface problem}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1631073X12002622},
volume = {350},
year = {2012}
}
@article{Wang2014,
author = {Wang, Qiuliang and Chen, Jinru},
doi = {10.1155/2014/241890},
issn = {1110-757X},
journal = {Journal of Applied Mathematics},
pages = {1--9},
title = {{An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems}},
url = {http://www.hindawi.com/journals/jam/2014/241890/},
volume = {2014},
year = {2014}
}
@article{Smith2007,
author = {Smith, Bryan G and {Vaughan Jr}, Benjamin L and Chopp, David L},
journal = {Communications in Applied Mathematics and Computational Science},
language = {english},
number = {1},
pages = {35--56},
title = {{The extended finite element method for boundary layer problems in biofilm grown}},
url = {http://pjm.math.berkeley.edu/camcos/2007/2-1/p02.xhtml},
volume = {2},
year = {2007}
}
@article {FreeFemPP,
AUTHOR = {Hecht, F.}, TITLE = {New development in FreeFem++},
JOURNAL = {J. Numer. Math.}, FJOURNAL = {Journal of Numerical Mathematics},
VOLUME = {20}, YEAR = {2012},
NUMBER = {3-4}, PAGES = {251--265},
ISSN = {1570-2820}, MRCLASS = {65Y15}, MRNUMBER = {3043640},
}
@thesis{Engwer2009,
author = {Engwer, Christian},
pages = {134},
school = {Ruprecht-Karls-Universit\"{a}t Heidelberg},
title = {{An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling}},
year = {2009}
}
@article{Szomolay,
author = {Szomolay, Barbara},
journal = {mbi.ohio-state.edu},
mendeley-groups = {biofilm},
pages = {1--19},
title = {{Analysis of a biofilm model}},
}
@thesis{szomolayThesis,
title={Analysis and control of a biofilm disinfection model},
author={Szomolay, Barbara and others},
year={2006},
school={Montana State University-Bozeman, College of Letters \& Science}
}
@article{potera1999,
title={Forging a link between biofilms and disease},
author={Potera, Carol},
year={1999},
publisher={American Association for the Advancement of Science}
}
@article{allison1995,
title={Modification by surface association of antimicrobial susceptibility of bacterial populations},
author={Allison, DG and Gilbert, P},
journal={Journal of industrial microbiology},
volume={15},
number={4},
pages={311--317},
year={1995},
publisher={Springer}
}
@thesis{Barrau2013,
author = {Barrau, Nelly},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/barrau/these de barrau.pdf:pdf},
mendeley-groups = {interface},
number = {10/2013},
pages = {197},
school = {Universite de Pau et des Pays de l'Adour},
title = {{G{\'{e}}n{\'{e}}ralisation de la m{\'{e}}thode Nitsche XFEM pour la discr{\'{e}}tisation de probl{\`{e}}mes d'interface elliptiques}},
year = {2013}
}
@book{LeDret2013,
address = {Berlin, Heidelberg},
author = {{Le Dret}, Herv{\'{e}}},
doi = {10.1007/978-3-642-36175-3},
isbn = {978-3-642-36174-6},
publisher = {Springer Berlin Heidelberg},
series = {Math{\'{e}}matiques et Applications},
title = {{{\'{E}}quations Aux D{\'{e}}riv{\'{e}}es Partielles Elliptiques Non Lin{\'{e}}aires}},
volume = {72},
year = {2013}
}
@article{George2000,
author = {George O'Toole and Heidi B. Kaplan and Roberto Kolter},
title = {Biofilm formation as microbial development},
journal ={Annual Review of Microbiology},
volume = {54},
pages = {49-79},
year = {2000}
}
@online{good,
author = {Alfred B. Cunningham and John E. Lennox and Rockford J. Ross},
title = {Biofilms: The hypertextbook},
year = {2010},
chapter = {1},
note = {\url{http://www.cs.montana.edu/webworks/projects/stevesbook/index.html}},
}
@book{Durr2009,
title={Biofouling},
author={D{\"u}rr, S. and Thomason, J.C.},
isbn={9781444315479},
url={https://books.google.fr/books?id=pERX3gKmFy4C},
year={2009},
publisher={Wiley}
}
@book{biofilmHypertext,
author = {Alfred B. Cunningham and John E. Lennox and Rockford J. Ross},
title = {Biofilms: The hypertextbook},
keywords = {biofilm},
posted-at = {2008-07-23 18:04:24},
year = {2010},
url = {http://www.erc.montana.edu/biofilmbook/}
}
@book{wannerBook,
author = {O. Wanner},
title = {Mathematical Modeling of Biofilms},
year = {2006},
publisher = {IWA Publishing},
address = {London},
}
@article{Ishihara1982,
author = {Ishihara, Kazuo},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/nonlinear - fixed - iterative - newton/kazou fem nonlinear .pdf:pdf},
journal = {Publ. RIMS, Lyoto Univ.},
pages = {17--34},
title = {{Finite Element Approximations Applied to the Nonlinear Boundary Value Problem $\Delta u=bu^2$}},
volume = {18},
year = {1982}
}
@article{johansson2011,
title={Implementation of a standard level set method for incompressible two-phase flow simulations},
author={Johansson, Niklas},
year={2011}
}
@book{Ern2004,
abstract = {an overview of standard and non standard finite element methods from$\backslash$ntheoritical foundations to implementations.},
author = {Ern, A. and Guermond, J.-L.},
doi = {10.1007/978-1-4757-4355-5},
isbn = {0-387-20574-8},
issn = {00255572},
pages = {xiv+524},
title = {{Theory and Practice of Finite Elements}},
volume = {159},
year = {2004}
}
@book{Rudin,
AUTHOR = {Rudin, Walter},
TITLE = {Real and complex analysis},
EDITION = {Third},
PUBLISHER = {McGraw-Hill Book Co.},
ADDRESS = {New York},
YEAR = {1987},
PAGES = {xiv+416},
ISBN = {0-07-054234-1},
MRCLASS = {00A05 (26-01 30-01 46-01)},
MRNUMBER = {MR924157 (88k:00002)},
}
@article{barrett1987,
title={Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces},
author={Barrett, John W and Elliott, Charles M},
journal={IMA journal of numerical analysis},
volume={7},
number={3},
pages={283--300},
year={1987},
publisher={Oxford University Press}
}
@book{Vasile2007,
author = {Berinde, Vasile},
doi = {10.1007/978-3-540-72234-2},
isbn = {9783540722335},
issn = {00758434},
publisher = {Springer},
title = {{Iterative Approximation of Fixed Points, Lecture Notes in Mathematics}},
year = {2007}
}
@article{Bui2011,
author = {Bui, Thi Thu Cuc and Frey, P. and Maury, B.},
doi = {10.1002/fld.2307},
issn = {02712091},
journal = {International Journal for Numerical Methods in Fluids},
keywords = {Advection,Finite element methods,Level sets,Mesh adaptation,Stokes equation,Two-fluid flows},
number = {10},
pages = {1226--1247},
title = {{A coupling strategy based on anisotropic mesh adaptation for solving two-fluid flows}},
volume = {66},
year = {2011}
}
@book{Hesthaven2008,
address = {New York, NY},
author = {Hesthaven, Jan S. and Warburton, Tim},
doi = {10.1007/978-0-387-72067-8},
editor = {Marsden, J.E. and Sirovich, L. and Antman, S.S.},
isbn = {978-0-387-72065-4},
publisher = {Springer New York},
series = {Texts in Applied Mathematics},
title = {{Nodal Discontinuous Galerkin Methods}},
volume = {54},
year = {2008}
}
@article{Sethian1996fast,
title={A fast marching level set method for monotonically advancing fronts},
author={Sethian, James A},
journal={Proceedings of the National Academy of Sciences},
volume={93},
number={4},
pages={1591--1595},
year={1996},
publisher={National Acad Sciences}
}
@book{Roos2008,
title={Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems},
author={Roos, Hans-G{\"o}rg and Stynes, Martin and Tobiska, Lutz},
volume={24},
year={2008},
publisher={Springer Science \& Business Media}
}
@book{ArnoldBook,
author = {Gross, S and Reusken, Arnold},
isbn = {9783642196850},
pages = {482},
series = {Springer Series in Computational Mathematics},
title = {{Numerical methods for two-phase incompressible flows}},
volume = {40},
year = {2011}
}
@article{Li1994iim,
title={The immersed interface method for elliptic equations with discontinuous coefficients and singular sources},
author={Leveque, Randall J and Li, Zhilin},
journal={SIAM Journal on Numerical Analysis},
volume={31},
number={4},
pages={1019--1044},
year={1994},
publisher={SIAM}
}
@article{Li2003iim,
author = {Li, Zhilin},
journal = {Taiwanese journal of mathematics},
number = {1},
pages = {1--49},
title = {{An overview of the immersed interface method and its applications}},
url = {http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/1112},
volume = {7},
year = {2003}
}
@article{Osher1988,
author = {Osher, Stanley and Sethian, James A},
doi = {10.1016/0021-9991(88)90002-2},
issn = {00219991},
journal = {Journal of Computational Physics},
month = {nov},
number = {1},
pages = {12--49},
title = {{Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations}},
volume = {79},
year = {1988}
}
@article{annavarapu2012,
title={A robust Nitsche’s formulation for interface problems},
author={Annavarapu, Chandrasekhar and Hautefeuille, Martin and Dolbow, John E},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={225},
pages={44--54},
year={2012},
publisher={Elsevier}
}
@article{Tornberg2000,
author = {Tornberg, Anna-Karin and Engquist, Bjorn},
doi = {10.1007/s007910050056},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/level set method/fem based level set method - Anna-Karin.pdf:pdf},
issn = {1432-9360},
journal = {Computing and Visualization in Science},
number = {1-2},
pages = {93--101},
title = {{A finite element based level-set method for multiphase flow applications}},
volume = {3},
year = {2000}
}
@article{Sussman1994,
arxivId = {1994},
author = {Sussman, Mark and Smereka, Peter and Osher, Stanley},
booktitle = {Journal of Computational Physics},
doi = {10.1006/jcph.1994.1155},
eprint = {1994},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/level set method/level set approach - sussman.pdf:pdf},
isbn = {0021-9991},
issn = {00219991},
number = {1},
pages = {146--159},
title = {{A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow}},
volume = {114},
year = {1994}
}
@techreport{Lehrenfeld2015,
address = {Vienna},
author = {Lehrenfeld, Christoph},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/xfem/xfem interface Christoph Lehrenfeld note.pdf:pdf},
institution = {Vienna University of Technology},
mendeley-groups = {level set method},
pages = {90},
title = {{Extended finite element methods for interface problems}},
year = {2015}
}
@article{Lehrenfeld2012,
author = {Lehrenfeld, Christoph and Reusken, Arnold},
doi = {10.1137/110855235},
file = {:Users/dinhanhthi/Library/Application Support/Mendeley Desktop/Downloaded/Lehrenfeld, Reusken - 2012 - Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem.pdf:pdf},
issn = {1064-8275},
journal = {SIAM Journal on Scientific Computing},
month = {jan},
number = {5},
pages = {A2740--A2759},
title = {{Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem}},
url = {http://epubs.siam.org/doi/abs/10.1137/110855235},
volume = {34},
year = {2012}
}
@article{belytschko99,
title={Elastic crack growth in finite elements with minimal remeshing},
author={Belytschko, Ted and Black, Tom},
journal={International journal for numerical methods in engineering},
volume={45},
number={5},
pages={601--620},
year={1999}
}
@article{Arnold2008,
author = {Reusken, Arnold},
doi = {10.1007/s00791-008-0099-8},
issn = {1432-9360},
journal = {Computing and Visualization in Science},
keywords = {extended finite element space,flow,spurious velocities,stokes equations in the,subdomains with the coupling,surface tension,two-phase},
month = {apr},
number = {4-6},
pages = {293--305},
title = {{Analysis of an extended pressure finite element space for two-phase incompressible flows}},
url = {http://link.springer.com/10.1007/s00791-008-0099-8},
volume = {11},
year = {2008}
}
@article{lehrenfeld2017optimal,
title={Optimal preconditioners for Nitsche-XFEM discretizations of interface problems},
author={Lehrenfeld, Christoph and Reusken, Arnold},
journal={Numerische Mathematik},
volume={135},
number={2},
pages={313--332},
year={2017},
publisher={Springer}
}
@techreport{DeVuyst2013,
author = {{De Vuyst}, Florian},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/freefem{\_}docs/numerical modeling transport problem with freefem - Florian De Vuyst.pdf:pdf},
institution = {ENS CACHAN},
pages = {162},
title = {{Numerical modeling of transport problems using freefem++ software -- with examples in biology, CFD, traffic flow and energy transfer}},
url = {http://cel.archives-ouvertes.fr/cel-00842234},
year = {2013}