An extended P1-nonconforming finite element method on general polytopal partitions

An extended P-1-nonconforming finite element method is developed in this article for the Dirichlet boundary value problem of convection-diffusion-reaction equations on general polytopal partitions. This new method was motivated by the simplified weak Galerkin method, and makes use of only the degrees of freedom on the boundary of each element and, hence, has reduced computational complexity. Numerical stability and optimal order of error estimates in H-1 and L-2 norms are established for the corresponding numerical solutions. Some numerical results are presented to computationally verify the mathematical convergence theory. A superconvergence phenomenon on rectangular partitions is noted and illustrated through various numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

An extended P-1 nonconforming finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations on general polytopal partitions, inspired by the simplified weak Galerkin method. The method reduces computational complexity by utilizing only the degrees of freedom on the boundary of each element. Numerical stability and optimal order of error estimates in H-1 and L-2 norms are established for the numerical solutions, with a superconvergence phenomenon noted on rectangular partitions through numerical experiments.