A LOCAL PROJECTION STABILIZATION FINITE ELEMENT METHOD WITH NONLINEAR CROSSWIND DIFFUSION FOR CONVECTION-DIFFUSION-REACTION EQUATIONS

被引：23

作者：

Barrenechea, Gabriel R. ^{[1
]}

John, Volker ^{[2
,3
]}

Knobloch, Petr ^{[4
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[2] Weierstrass Inst Appl Anal & Stochast WIAS, D-10117 Berlin, Germany

[3] Free Univ Berlin, Dept Math & Comp Sci, D-14195 Berlin, Germany

[4] Charles Univ Prague, Dept Numer Math, Fac Math & Phys, Prague 18675 8, Czech Republic

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2013年 / 47卷 / 05期

关键词：

Finite element method; local projection stabilization; crosswind diffusion; convection-diffusion-reaction equation; well posedness; time dependent problem; stability; error estimates; DIMINISHING SOLD METHODS; SPURIOUS OSCILLATIONS;

D O I：

10.1051/m2an/2013071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

引用

页码：1335 / 1366

页数：32

共 32 条

[1] An assessment of discretizations for convection-dominated convection-diffusion equations [J].

Augustin, Matthias ;

Caiazzo, Alfonso ;

Fiebach, Andre ;

Fuhrmann, Juergen ;

John, Volker ;

Linke, Alexander ;

Umla, Rudolf .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (47-48) :3395-3409

[2] A finite element pressure gradient stabilization for the Stokes equations based on local projections [J].

Becker, R ;

Braack, M .

CALCOLO, 2001, 38 (04) :173-199

[3]

Becker R., 2004, P ENUMATH 2003 NUM M, P123

[4] Stabilized finite element methods for the generalized Oseen problem [J].

Braack, M. ;

Burman, E. ;

John, V. ;

Lube, G. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (4-6) :853-866

[5] Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method [J].

Braack, M ;

Burman, E .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 43 (06) :2544-2566

[6] STREAMLINE UPWIND PETROV-GALERKIN FORMULATIONS FOR CONVECTION DOMINATED FLOWS WITH PARTICULAR EMPHASIS ON THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].

BROOKS, AN ;

HUGHES, TJR .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1982, 32 (1-3) :199-259

[7] Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence [J].

Burman, E ;

Ern, A .

MATHEMATICS OF COMPUTATION, 2005, 74 (252) :1637-1652

[8] Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems [J].

Burman, E ;

Hansbo, P .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (15-16) :1437-1453

[9] Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation [J].

Burman, Erik ;

Fernandez, Miguel A. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2009, 198 (33-36) :2508-2519

[10]

CIARLET P. G., 2002, Classics in Appl. Math., V40

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