Multigrid for an HDG method

被引：55

作者：

Cockburn, B. ^{[1
]}

Dubois, O. ^{[2
]}

Gopalakrishnan, J. ^{[3
]}

Tan, S. ^{[4
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Ecole Polytech Montreal, Quebec City, PQ, Canada

[3] Portland State Univ, Portland, OR 97207 USA

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2014年 / 34卷 / 04期

基金：

美国国家科学基金会;

关键词：

multigrid methods; discontinuous Galerkin methods; hybrid methods; DISCONTINUOUS GALERKIN APPROXIMATIONS; ELLIPTIC PROBLEMS; ERROR ANALYSIS; MIXED METHODS; ALGORITHMS; PRECONDITIONERS; CONVERGENCE; CYCLE;

D O I：

10.1093/imanum/drt024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyse the convergence of a multigrid algorithm for the hybridizable discontinuous Galerkin (HDG) method for diffusion problems. We prove that a nonnested multigrid V-cycle, with a single smoothing step per level, converges at a mesh-independent rate. Along the way, we study conditioning of the HDG method, prove new error estimates for it and identify an abstract class of problems for which a non-nested two-level multigrid cycle with one smoothing step converges even when the prolongation norm is greater than 1. Numerical experiments verifying our theoretical results are presented.

引用

页码：1386 / 1425

页数：40

共 39 条

[11]

Brenner SC, 2004, MATH COMPUT, V73, P1041

[12] Convergence of nonconforming multigrid methods without full elliptic regularity [J].