ADAPTIVE VIRTUAL ELEMENT METHOD FOR CONVECTION DOMINATED DIFFUSION EQUATIONS

被引：0

作者：

Wang, Qiming ^{[1
]}

Zhou, Zhaojie ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2025年 / 43卷 / 01期

基金：

中国国家自然科学基金;

关键词：

A posteriori estimate; SUPG virtual element method; Convection dominated diffusion equation; Adaptive VEM algorithm; SUPG STABILIZATION; FORMULATION; PENALTY;

D O I：

10.4208/jcm.2309-m2021-0366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of convection dominated diffusion equation. A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm, where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors. Based on the Dorfler's marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes. Numerical experiments show the robustness of the a posteriori error estimates.

引用

页码：174 / 202

页数：29

共 37 条

[21] A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem [J].

Deng, Yanling ;

Wang, Fei ;

Wei, Huayi .

JOURNAL OF SCIENTIFIC COMPUTING, 2020, 83 (03)

[22] A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems [J].

Egger, Herbert ;

Schoeberl, Joachim .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2010, 30 (04) :1206-1234

[23]

El Alaoui L, 2007, IMA J NUMER ANAL, V27, P151, DOI [10.1093/imanum/dr1011, 10.1093/imanum/drl011]

[24] STABILIZED FINITE-ELEMENT METHODS .1. APPLICATION TO THE ADVECTIVE-DIFFUSIVE MODEL [J].

FRANCA, LP ;

FREY, SL ;

HUGHES, TJR .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 95 (02) :253-276

[25] UNIFORM SUPERCONVERGENCE OF A FINITE ELEMENT METHOD WITH EDGE STABILIZATION FOR CONVECTION-DIFFUSION PROBLEMS [J].

Franz, Sebastian ;

Linss, Torsten ;

Roos, Hans-Goerg ;

Schiller, Sebastian .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2010, 28 (01) :32-44

[26] A MIXED VIRTUAL ELEMENT METHOD FOR THE BOUSSINESQ PROBLEM ON POLYGONAL MESHES [J].

Gatica, Gabriel N. ;

Munar, Mauricio ;

Sequeira, Filander A. .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2021, 39 (03) :392-427

[27]

Hinze M, 2009, J COMPUT MATH, V27, P237

[28] A robust SUPG norm a posteriori error estimator for stationary convection-diffusion equations [J].

John, Volker ;

Novo, Julia .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2013, 255 :289-305

[29]

Manzini G., 2014, Technical Report, LA-UR-14-27710

[30] A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations [J].

Mora, David ;

Rivera, Gonzalo .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2020, 40 (01) :322-357

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