A new stabilized finite element method for advection-diffusion-reaction equations

被引：6

作者：

Duan, Huoyuan ^{[1
]}

Qiu, Fengjuan ^{[2
]}

机构：

[1] Wuhan Univ, Computat Sci Hubei Key Lab, Collaborat Innovat Ctr Math, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Bank China, Beijing, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 32卷 / 02期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

advection-diffusion-reaction equation; boundary-layer; error estimates; large reaction; small diffusivity; stabilized finite element method; RESIDUAL-FREE BUBBLES; DIMINISHING SOLD METHODS; NAVIER-STOKES EQUATIONS; LEAST-SQUARES METHOD; SPURIOUS OSCILLATIONS; FORMULATIONS; MULTISCALE;

D O I：

10.1002/num.22021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, a new stabilized finite element method is proposed and analyzed for advection-diffusion-reaction equations. The key feature is that both the mesh-dependent Peclet number and the mesh-dependent Damkohler number are reasonably incorporated into the newly designed stabilization parameter. The error estimates are established, where, up to the regularity-norm of the exact solution, the explicit-dependence of the diffusivity, advection, reaction, and mesh size (or the dependence of the mesh-dependent Peclet number and the mesh-dependent Damkohler number) is revealed. Such dependence in the error bounds provides a mathematical justification on the effectiveness of the proposed method for any values of diffusivity, advection, dissipative reaction, and mesh size. Numerical results are presented to illustrate the performance of the method. (c) 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 616-645, 2016

引用

页码：616 / 645

页数：30

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