TY - JOUR
T1 - Error Analysis of Linearized Semi-Implicit Galerkin Finite Element Methods for Nonlinear Parabolic Equations
AU - B. Li & W. Sun
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 622
EP - 633
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/586.html
KW - Nonlinear parabolic system, unconditionally optimal error estimate, linearized semi-implicit scheme, Galerkin method.
AB - <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>