@Article{IJNAM-10-622,
author = {B. Li and W. Sun},
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 = {<p style="text-align: justify;">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 $\tau$.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/586.html}
}