Patch‐wise local projection stabilized finite element methods for convection–diffusion–reaction problems

Abstract

In this article, we develop patch-wise local projection-stabilized conforming and nonconforming finite element methods for the convection–diffusion–reaction problems. It is a composition of the standard Galerkin finite element method, the patch-wise local projection stabilization, and weakly imposed Dirichlet boundary conditions on the discrete solution. In this paper, a priori error analysis is established with respect to a patch-wise local projection norm for the conforming and the nonconforming finite element methods. The numerical experiments confirm the efficiency of the proposed stabilization technique and validate the theoretical convergence rates.