Volume 8, Issue 4
A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces

Liqun Wang & Liwei Shi

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 475-495.

Published online: 2015-08

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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.

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@Article{NMTMA-8-475, author = {}, title = {A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {4}, pages = {475--495}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1331}, url = {http://global-sci.org/intro/article_detail/nmtma/12419.html} }
TY - JOUR T1 - A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 475 EP - 495 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.m1331 UR - https://global-sci.org/intro/article_detail/nmtma/12419.html KW - AB -

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.

Liqun Wang & Liwei Shi. (2020). A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces. Numerical Mathematics: Theory, Methods and Applications. 8 (4). 475-495. doi:10.4208/nmtma.2015.m1331
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