Discontinuous Galerkin methods for anisotropic semidefinite diffusion with advection

被引：53

作者：

Di Pietro, Daniele A. ^{[1
]}

Ern, Alexandre ^{[1
]}

Guermond, Jean-Luc ^{[2
,3
]}

机构：

[1] Univ Paris Est, Ecole Ponts, CERMICS, F-77455 Marne La Vallee 2, France

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

[3] LIMSI, CNRS, UPR 3251, F-91403 Orsay, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 02期

关键词：

discontinuous Galerkin; advection-diffusion-reaction; discontinuous coefficients; anisotropic diffusion; coupled elliptic-hyperbolic; weighted averages;

D O I：

10.1137/060676106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct and analyze a discontinuous Galerkin method to solve advection-diffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consistent with well-known results when the problem is either hyperbolic or uniformly elliptic. The theoretical results are supported by numerical evidence.

引用

页码：805 / 831

页数：27

共 26 条

[1]

ANROLD DN, 1985, RAIRO MODEL MATH ANA, V19, P7

[2] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[3] AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS [J].

ARNOLD, DN .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) :742-760

[4]

BAKER GA, 1977, MATH COMPUT, V31, P45, DOI 10.1090/S0025-5718-1977-0431742-5

[5]

Bassi F., 1997, P 2 EUR C TURB FLUID, P99

[6] A domain decomposition method based on weighted interior penalties for advection-diffusion-reaction problems [J].

Burman, Erik ;

Zunino, Paolo .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (04) :1612-1638

[7] The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].

Cockburn, B ;

Shu, CW .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463

[8]

Croisille J.-P., 2005, Journal of Numerical Mathematics, V13, P81, DOI 10.1163/1569395054012776

[9] Discontinuous Galerkin methods for Friedrichs' systems. I. General theory [J].

Ern, A. ;

Guermond, J. -L. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (02) :753-778

[10]

ERN A, IN PRESS IMA J NUMER

← 1 2 3 →