A Conforming Discontinuous Galerkin Finite Element Method: Part II

Authors

  • Xiu Ye Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA.
  • Shangyou Zhang Department of Mathematics Science, University of Delaware, Newark 19716, USA

Keywords:

Weak Galerkin, discontinuous Galerkin, stabilizer/penalty free, finite element methods, second order elliptic problem.

Abstract

A conforming discontinuous Galerkin (DG) finite element method has been introduced in [19] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous finite element method. The goal of this paper is to extend the conforming DG finite element method in [19] so that it can work on general polytopal meshes by designing weak gradient ∇$w$ appropriately. Two different conforming DG formulations on polytopal meshes are introduced which handle boundary conditions differently. Error estimates of optimal order are established for the corresponding conforming DG approximation in both a discrete $H$1 norm and the $L$2 norm. Numerical results are presented to confirm the theory.

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Published

2020-02-03

Issue

Vol. 17 No. 2 (2020)

Section

Articles