A network element method for heterogeneous and anisotropic diffusion-reaction problems

Abstract

The network element method (NEM), a variational numerical method where the usual mesh was replaced by a discretization network has been recently introduced for the basic Poisson problem. A coercive and stable numerical scheme was proposed, and a convergence theory leading to convergence for minimal regularity solutions was derived, along with error estimates. The aim of the present paper is to explain how the method can be extended to the more general case of heterogeneous and anisotropic diffusion-reaction problems, as well as providing updated error estimates. Numerical experiments illustrate the good behavior of the method even for low regularity solutions with discontinuous diffusion coefficients.