A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients
Year: 2019
Author: Liqun Wang, Songming Hou, Liwei Shi, Ping Zhang
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 216–240
Abstract
In this paper, a bilinear Petrov-Galerkin finite element method is introduced to solve the variable matrix coefficient elliptic equation with interfaces using non-body-fitted grid. Different cases the interface cut the cell are discussed. The condition number of the large sparse linear system is studied. Numerical results demonstrate that the method is nearly second order accurate in the $L^\infty$ norm and $L^2$ norm, and is first order accurate in the $H^1$ norm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0099
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 1 : pp. 216–240
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Petrov-Galerkin finite element method jump condition bilinear.
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