Optimal Error Analysis of Galerkin FEMs for Nonlinear Joule Heating Equations

被引：59

作者：

Gao, Huadong ^{[1
]}

机构：

[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2014年 / 58卷 / 03期

关键词：

Nonlinear parabolic system; Unconditional convergence; Optimal error estimate; Linearized semi-implicit scheme; Galerkin method; NAVIER-STOKES EQUATIONS; FINITE-ELEMENT APPROXIMATION; THERMISTOR EQUATIONS; POROUS-MEDIA; MISCIBLE DISPLACEMENT; CONVERGENCE ANALYSIS; TIME-DISCRETIZATION; SPECTRAL METHOD; EXISTENCE;

D O I：

10.1007/s10915-013-9746-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study in this paper two linearized backward Euler schemes with Galerkin finite element approximations for the time-dependent nonlinear Joule heating equations. By introducing a time-discrete (elliptic) system as proposed in Li and Sun (Int J Numer Anal Model 10:622-633, 2013; SIAM J Numer Anal (to appear)), we split the error function as the temporal error function plus the spatial error function, and then we present unconditionally optimal error estimates of th order Galerkin FEMs (). Numerical results in two and three dimensional spaces are provided to confirm our theoretical analysis and show the unconditional stability (convergence) of the schemes.

引用

页码：627 / 647

页数：21

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