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Volume 11, Issue 1
A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients

Liqun Wang, Songming Hou, Liwei Shi & Ping Zhang

Adv. Appl. Math. Mech., 11 (2019), pp. 216-240.

Published online: 2019-01

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  • 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.

  • AMS Subject Headings

65N30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-11-216, author = {Wang , LiqunHou , SongmingShi , Liwei and Zhang , Ping}, title = {A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0099}, url = {http://global-sci.org/intro/article_detail/aamm/12929.html} }
TY - JOUR T1 - A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients AU - Wang , Liqun AU - Hou , Songming AU - Shi , Liwei AU - Zhang , Ping JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 216 EP - 240 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0099 UR - https://global-sci.org/intro/article_detail/aamm/12929.html KW - Petrov-Galerkin finite element method, jump condition, bilinear. AB -

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.

Wang , LiqunHou , SongmingShi , Liwei and Zhang , Ping. (2019). A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients. Advances in Applied Mathematics and Mechanics. 11 (1). 216-240. doi:10.4208/aamm.OA-2018-0099
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