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Rate of Convergence for a Fully-Discrete Reliable Scheme for a System of Nonlinear Time-Dependent Joule Heating Equations |
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PP: 997-1007 |
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doi:10.18576/amis/100317
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Author(s) |
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Pius W. M. Chin,
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Abstract |
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| 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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