@Article{IJNAM-10-622, author = {}, title = {Error Analysis of Linearized Semi-Implicit Galerkin Finite Element Methods for Nonlinear Parabolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {622--633}, 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 applicable 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 $\tau$.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/586.html} }