Volume 10, Issue 3
Error Analysis of Linearized Semi-implicit Galerkin Finite Element Methods for Nonlinear Parabolic Equations

B. Li & W. Sun

DOI:

Int. J. Numer. Anal. Mod., 10 (2013), pp. 622-633

Published online: 2013-10

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  • Abstract

This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the L^2 norm and the H^1 norm without any time-step restriction. Theoretical analysis is based on a new splitting of error function and precise analysis of a corresponding time-discrete system. The method used in this paper is appli- cable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations for which previous works often require certain restriction on the time-step size .

  • Keywords

Nonlinear parabolic system unconditionally optimal error estimate linearized semi-implicit scheme Galerkin method

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