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A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  10 November 2015

Liqun Wang  and
Liwei Shi
Liqun Wang
Affiliation:
Department of Mathematics, China University of Petroleum (Beijing), Beijing, 102249, China
Liwei Shi*
Affiliation:
Department of Science and Technology Teaching, China University of Political Science and Law, Beijing, 102249, China
*
*Corresponding author. Email addresses: [email protected] (L.-Q. Wang), [email protected] (L.-W. Shi)
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Abstract

In this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. Extensive numerical experiments illustrate the feasibility of the method.

Keywords

Heat equationSharp-edged interfaceJump conditionMatrix coefficient

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 4 , November 2015 , pp. 475 - 495
Copyright
Copyright © Global-Science Press 2015 

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