Optimal Error Analysis of Galerkin FEMs for Nonlinear Joule Heating Equations

Authors:
Huadong Gao
Affiliations:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Venue:
Journal of Scientific Computing
Year:
2014

Citing 12
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Abstract

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 $$r$$rth order Galerkin FEMs ($$1 \le r \le 3$$1≤r≤3). Numerical results in two and three dimensional spaces are provided to confirm our theoretical analysis and show the unconditional stability (convergence) of the schemes.