Try #1392:

src/Geometry/conversions.jl

@@ -7,7 +7,7 @@
 ContravariantVector(u::ContravariantVector, ::LocalGeometry) = u
 CovariantVector(u::CovariantVector, ::LocalGeometry) = u
 LocalVector(u::LocalVector, ::LocalGeometry) = u
-
+# conversions between Covariant/Contravariant vectors and local vectors
 ContravariantVector(
     u::LocalVector{T, I},
     local_geometry::LocalGeometry{I},
@@ -25,6 +25,29 @@ LocalVector(
     local_geometry::LocalGeometry{I},
 ) where {T, I} = local_geometry.∂ξ∂x' * u
 
+# conversions between Covariant and Contravariant vectors
+Contravariant123Vector(
+    u::CovariantVector{T, (1, 2)},
+    local_geometry::LocalGeometry{(1, 2, 3)},
+) where {T} = local_geometry.gⁱʲ * Covariant123Vector(u[1], u[2], zero(u[1]))
+
+Contravariant123Vector(
+    u::CovariantVector{T, (3,)},
+    local_geometry::LocalGeometry{(1, 2, 3)},
+) where {T} =
+    local_geometry.gⁱʲ * Covariant123Vector(zero(u[1]), zero(u[1]), u[1])
+
+
+ContravariantVector(
+    u::CovariantVector{T, I},
+    local_geometry::LocalGeometry{I},
+) where {T, I} = local_geometry.gⁱʲ * u
+
+CovariantVector(
+    u::ContravariantVector{T, I},
+    local_geometry::LocalGeometry{I},
+) where {T, I} = local_geometry.gᵢⱼ * u
+
 # Converting to specific dimension types
 (::Type{<:ContravariantVector{<:Any, I}})(
     u::ContravariantVector{<:Any, I},

src/Geometry/localgeometry.jl

@@ -19,11 +19,22 @@ struct LocalGeometry{I, C <: AbstractPoint, FT, S}
     ∂ξ∂x::Axis2Tensor{FT, Tuple{ContravariantAxis{I}, LocalAxis{I}}, S}
     "Contravariant metric tensor (inverse of gᵢⱼ), transforms covariant to contravariant vector components"
     gⁱʲ::Axis2Tensor{FT, Tuple{ContravariantAxis{I}, ContravariantAxis{I}}, S}
+    "Covariant metric tensor (gᵢⱼ), transforms contravariant to covariant vector components"
+    gᵢⱼ::Axis2Tensor{FT, Tuple{CovariantAxis{I}, CovariantAxis{I}}, S}
 end
 
 @inline function LocalGeometry(coordinates, J, WJ, ∂x∂ξ)
     ∂ξ∂x = inv(∂x∂ξ)
-    return LocalGeometry(coordinates, J, WJ, inv(J), ∂x∂ξ, ∂ξ∂x, ∂ξ∂x * ∂ξ∂x')
+    return LocalGeometry(
+        coordinates,
+        J,
+        WJ,
+        inv(J),
+        ∂x∂ξ,
+        ∂ξ∂x,
+        ∂ξ∂x * ∂ξ∂x',
+        ∂x∂ξ' * ∂x∂ξ,
+    )
 end
 
 """