Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II - Quantitative Studies

被引：0

作者：

Brix, Kolja ^{[1
]}

Pinto, Martin Campos ^{[2
]}

Dahmen, Wolfgang ^{[1
]}

Massjung, Ralf ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Inst Geometrie & Prakt Math, D-52056 Aachen, Germany

[2] Univ Strasbourg, CNRS, UMR 7501, Inst Rech Math Avancee, F-67084 Strasbourg, France

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2009年 / 5卷 / 2-4期

关键词：

Interior penalty method; energy-stable splittings; admissible averaging operators; frames; multilevel Schwarz preconditioners; discontinuous Galerkin methods; APPROXIMATIONS; DECOMPOSITION;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper is concerned with preconditioners for interior penalty discontinuous Galerkin discretizations of second-order elliptic boundary value problems. We extend earlier related results in [7] in the following sense. Several concrete realizations of splitting the nonconforming trial spaces into a conforming and (remaining) nonconforming part are identified and shown to give rise to uniformly bounded condition numbers. These asymptotic results are complemented by numerical tests that shed some light on their respective quantitative behavior.

引用

页码：296 / 325

页数：30

共 49 条

[31] Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems
Barker, A. T.
Brenner, S. C.
Sung, L. -Y.
JOURNAL OF NUMERICAL MATHEMATICS, 2011, 19 (03) : 165 - 187
[32] A Discontinuous Galerkin Method with Penalty for One-Dimensional Nonlocal Diffusion Problems
Du, Qiang
Ju, Lili
Lu, Jianfang
Tian, Xiaochuan
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2020, 2 (01) : 31 - 55
[33] A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems
Georgoulis, EH
Lasis, A
IMA JOURNAL OF NUMERICAL ANALYSIS, 2006, 26 (02) : 381 - 390
[34] Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow
Feng, Xiaobing
Li, Yukun
IMA JOURNAL OF NUMERICAL ANALYSIS, 2015, 35 (04) : 1622 - 1651
[35] A C0 interior penalty discontinuous Galerkin method for fourth-order total variation flow. I: Derivation of the method and numerical results
Bhandari, Chandi
Hoppe, Ronald H. W.
Kumar, Rahul
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (04) : 1458 - 1476
[36] A Multi-modes Monte Carlo Interior Penalty Discontinuous Galerkin Method for the Time-Harmonic Maxwell's Equations with Random Coefficients
Feng, Xiaobing
Lin, Junshan
Lorton, Cody
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 80 (03) : 1498 - 1528
[37] A Multi-modes Monte Carlo Interior Penalty Discontinuous Galerkin Method for the Time-Harmonic Maxwell’s Equations with Random Coefficients
Xiaobing Feng
Junshan Lin
Cody Lorton
Journal of Scientific Computing, 2019, 80 : 1498 - 1528
[38] Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method
Zhou, Zhenhua
Wu, Haijun
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2016, 9 (01) : 51 - 86
[39] hp-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
Mozolevski, Igor
Sueli, Endre
Boesing, Paulo R.
JOURNAL OF SCIENTIFIC COMPUTING, 2007, 30 (03) : 465 - 491
[40] hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation
Igor Mozolevski
Endre Süli
Paulo R. Bösing
Journal of Scientific Computing, 2007, 30 : 465 - 491

← 1 2 3 4 5 →