OPTIMAL ERROR ESTIMATES IN THE DG METHOD FOR NONLINEAR CONVECTION-DIFFUSION PROBLEMS

被引：0

作者：

Kucera, Vaclav ^{[1
]}

机构：

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

来源：

ALGORITMY 2009: 18TH CONFERENCE ON SCIENTIFIC COMPUTING | 2009年

关键词：

convection-diffusion equation; nonlinear diffusion; discontinuous Galerkin finite element method; optimal error estimates; DISCONTINUOUS GALERKIN METHOD;

D O I：

暂无

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper is concerned with the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonstationary convection-diffusion problem with nonlinear convection and nonlinear diffusion. Optimal estimates in the L(infinity)(L(2))-norm are derived for the symmetric interior penalty (SIPG) scheme in two dimensions. The error analysis is carried out for nonconforming triangular meshes under the assumption that the exact solution of the problem and the solution of a linearised elliptic dual problem are sufficiently regular.

引用

页码：236 / 245

页数：10

共 50 条

[1] Optimal L(L2)-Error Estimates for the DG Method Applied to Nonlinear Convection-Diffusion Problems with Nonlinear Diffusion
Kucera, Vaclav
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2010, 31 (03) : 285 - 312
[2] Optimal Error Estimates for Semi-implicit DG Time Discretization of Convection-Diffusion Problems
Vlasak, Miloslav
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
[3] Error estimates of the discontinuous Galerkin method for nonlinear nonstationary convection-diffusion problems
Dolejsí, V
Feistauer, M
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (03) : 349 - 383
[4] DISCONTINUOUS GALERKIN METHOD FOR NONSTATIONARY NONLINEAR CONVECTION-DIFFUSION PROBLEMS: A PRIORI ERROR ESTIMATES
Hozman, Jiri
ALGORITMY 2009: 18TH CONFERENCE ON SCIENTIFIC COMPUTING, 2009, : 294 - 303
[5] A posteriori error estimates for optimal control problems constrained by convection-diffusion equations
Fu, Hongfei
Rui, Hongxing
Zhou, Zhaojie
FRONTIERS OF MATHEMATICS IN CHINA, 2016, 11 (01) : 55 - 75
[6] A posteriori error estimates for optimal control problems constrained by convection-diffusion equations
Hongfei Fu
Hongxing Rui
Zhaojie Zhou
Frontiers of Mathematics in China, 2016, 11 : 55 - 75
[7] Nonlinear convection-diffusion problems: fully discrete approximations and a posteriori error estimates
De Frutos, Javier
Garcia-Archilla, Bosco
Novo, Julia
IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (04) : 1402 - 1430
[8] Error estimates for a combined finite volume-finite element method for nonlinear convection-diffusion problems
Feistauer, M
Felcman, J
Lukácová-Medvid'ová, M
Warnecke, G
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (05) : 1528 - 1548
[9] OPTIMAL ERROR ESTIMATES OF THE DIRECT DISCONTINUOUS GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS
Liu, Hailiang
MATHEMATICS OF COMPUTATION, 2015, 84 (295) : 2263 - 2295
[10] Error estimates for a combined finite volume-finite element method for nonlinear convection-diffusion problems
Feistauer, Miloslav
Felcman, Jiri
Lukacova-Medvid'Ova, Maria
Warnecke, Gerald
SIAM Journal on Numerical Analysis, 36 (05): : 1528 - 1548

← 1 2 3 4 5 →