Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation

Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation

Year:    2018

Author:    Fei Wang, Shuo Zhang

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 5 : pp. 693–717

Abstract

In this paper, we study Nitsche extended finite element method (XFEM) for the interface problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM can be implemented then.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1703-m2015-0340

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 5 : pp. 693–717

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Interface problems Extended finite element methods Error estimates Nitsche's scheme Quadratic element.

Author Details

Fei Wang

Shuo Zhang

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