Anders Logg <[email protected]> writes: > I also don't see the point in defining jump(v, n) for vector valued u > as in the paper. If the result of jump(v, n) is a scalar quantity, > there is no way to combine the normal n with the thing it should > naturally be paired with, namely the flux (or grad(u)). It only works > out in the special case of scalar elements.
The point of the definition in the paper is that "flux" or gradient jumps are dotted with the normal (thus reducing their rank). The overload in FEniCS is problematic because a multi-component "vector" (which just happens to have the same number of components as the gradient of a scalar) is being confused with the one-form (a covector). Note that while a vector (as in DG formulations for elasticity or Stokes) is contravariant, 3-species diffusion has the same dimensions, but is invariant. It may be more effort than it's worth to distinguish contravariant, covariant, and invariant "vectors" in the type system, but doing so would fix these ambiguities.
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