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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 3


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

PP: 997-1007
Pius W. M. Chin,
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.

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