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.

  • Keywords

Petrov-Galerkin finite element method jump condition bilinear.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-216, author = {Liqun Wang, Songming Hou, Liwei Shi and Ping Zhang}, 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} }
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