An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems
Abstract
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from discontinuous functions to continuous ones, and adopts piecewise polynomials of equal degrees on simplex meshes for all variables. In this paper, we analyze a new EDG method for second order elliptic problems on polygonal/polyhedral meshes. By using piecewise polynomials of degrees , , () to approximate the potential, numerical trace and flux, respectively, the new method is shown to yield optimal convergence rates for both the potential and flux approximations. Numerical experiments are provided to confirm the theoretical results.
Cite
@article{arxiv.1711.05544,
title = {An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems},
author = {Xiao Zhang and Xiaoping Xie and Shiquan Zhang},
journal= {arXiv preprint arXiv:1711.05544},
year = {2017}
}