Rate of Convergence for a Fully-Discrete Reliable Scheme for a System of Nonlinear Time-Dependent Joule Heating Equations

Authors

Pius W. M. Chin, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

An initial-boundary value problem for a system of decoupled two nonlinear time-dependent Joule heating equations is studied. Instead of well-known standard techniques, we design a reliable scheme consisting of coupling the non-standard finite difference (NSFD) method in time and finite element method (FEM) in space. We prove the rate of convergence for the fully-discrete scheme in both H1 as well as the L2-norms. Furthermore, we show that the above scheme preserves the properties of the exact solution. Numerical experiments are provided to confirm our theoretical analysis.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100317

Recommended Citation

W. M. Chin, Pius (2016) "Rate of Convergence for a Fully-Discrete Reliable Scheme for a System of Nonlinear Time-Dependent Joule Heating Equations," Applied Mathematics & Information Sciences: Vol. 10: Iss. 3, Article 17.
DOI: http://dx.doi.org/10.18576/amis/100317
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss3/17