We propose a discrete weighted Helmholtz decomposition for edge element functions. The decomposition is orthogonal in a weighted L inner product and stable uniformly with respect to the jumps in the discontinuous weight function. As an application, the new Helmholtz decomposition is applied to demonstrate the quasi-optimality of a preconditioned edge element system for solving a saddle-point Ma...

It is well known that the two-point flux approximation, a numerical scheme used in most commercial reservoir simulators, has O(1) error when grids are not K-orthogonal. In the last decade, multi-point flux approximations have been developed as a remedy. However, nonphysical oscillations can appear when the anisotropy is really strong. We found out the oscillations are closely related to the poo...