期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 47, 期 4, 页码 2686-2707出版社
SIAM PUBLICATIONS
DOI: 10.1137/080726914
关键词
finite element methods; mixed methods; discontinuous Galerkin methods; Lagrange multipliers
资金
- National Science Foundation [DMS-0712955, DMS-0503050]
- University of Minnesota Supercomputing Institute
The embedded discontinuous Galerkin methods are obtained from hybridizable discontinuous Galerkin methods by a simple change of the space of the hybrid unknown. In this paper, we consider embedded methods for second-order elliptic problems obtained from hybridizable discontinuous methods by changing the space of the hybrid unknown from discontinuous to continuous functions. This change results in a significantly smaller stiffness matrix whose size and sparsity structure coincides with those of the stiffness matrix of the statically condensed continuous Galerkin method. It is shown that this computational advantage has to be balanced against the fact that the approximate solutions for the scalar variable and its flux lose each a full order of convergence. Indeed, we prove that if polynomials of degree k >= 1 are used for the original hybridizable discontinuous Galerkin method, its approximations to the scalar variable and its flux converge with order k + 2 and k + 1, respectively, whereas those of the corresponding embedded discontinuous Galerkin method converge with orders k + 1 and k, respectively, only. We also provide numerical results comparing the relative efficiency of the methods.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据