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. [ABSTRACT FROM AUTHOR]