This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
The formulas for mapping_covariant_gradient, mapping_contravariant_gradient and mapping_piola_gradient are only true as stated for linear mappings. If, for example, the mapping is bilinear (or has a higher order polynomial degree) then there is a missing term associated with the derivative of \(J\).
Currently, we are storing an object for the cells and two for each face. We could gather all face data pertaining to the cell itself in one object, saving a bit of memory and a few operations, but sacrificing some cleanliness.