A conforming discontinuous Galerkin finite element method for elliptic interface problems

A new conforming discontinuous Galerkin method, which is based on weak Galerkin finite element method, is introduced for solving second order elliptic interface problems with discontinuous coefficient. The numerical method studied in this paper has no stabilizer and fewer unknowns compared with the known weak Galerkin algorithms. The error estimates in H-1 and L-2 norms are established, which are the optimal order convergence. Numerical experiments demonstrate the performance of the method, confirm the theoretical results of accuracy. (c) 2022 Elsevier B.V. All rights reserved.