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

Liqun Wang ,  Songming Hou ,  Liwei Shi and Ping Zhang

10.4208/aamm.OA-2018-0099

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

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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.

  • History

Published online: 2019-01

  • AMS Subject Headings

65N30

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