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Volume 36, Issue 5
Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation

Fei Wang & Shuo Zhang

DOI: 10.4208/jcm.1703-m2015-0340

J. Comp. Math., 36 (2018), pp. 693-717.

Published online: 2018-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N30, 65N12, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

feiwang.xjtu@xjtu.edu.cn (Fei Wang)

szhang@lsec.cc.ac.cn (Shuo Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-693, author = {Wang , Fei and Zhang , Shuo}, title = {Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1703-m2015-0340}, url = {http://global-sci.org/intro/article_detail/jcm/12453.html} }
TY - JOUR T1 - Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation AU - Wang , Fei AU - Zhang , Shuo JO - Journal of Computational Mathematics VL - 5 SP - 693 EP - 717 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1703-m2015-0340 UR - https://global-sci.org/intro/article_detail/jcm/12453.html KW - Interface problems, Extended finite element methods, Error estimates, Nitsche's scheme, Quadratic element. AB -

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.

Fei Wang & Shuo Zhang. (2020). Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation. Journal of Computational Mathematics. 36 (5). 693-717. doi:10.4208/jcm.1703-m2015-0340
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