Volume 12, Issue 4
A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems

Nan Wang & Jinru Chen

Adv. Appl. Math. Mech., 12 (2020), pp. 879-901.

Published online: 2020-06

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  • Abstract

This article proposes a new $P_{1}$ nonconforming Nitsche's extended finite element method for elliptic interface problems with interface-unfitted meshes. It is shown that the stability of the discrete formulation is independent of not only the mesh size and the diffusion parameters, but also the position of the interface, showing a robustness over the location of interface. In spite of the low regularity of interface problems, the optimal convergence is obtained. Numerical experiments are carried out to validate theoretical results.

  • Keywords

Nonconforming extended finite element, Nitsche's method, elliptic interface problems, interface-unfitted mesh.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

18260624492@163.com (Nan Wang)

jrchen@njnu.edu.cn (Jinru Chen)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-879, author = {Wang , Nan and Chen , Jinru }, title = {A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {4}, pages = {879--901}, abstract = {

This article proposes a new $P_{1}$ nonconforming Nitsche's extended finite element method for elliptic interface problems with interface-unfitted meshes. It is shown that the stability of the discrete formulation is independent of not only the mesh size and the diffusion parameters, but also the position of the interface, showing a robustness over the location of interface. In spite of the low regularity of interface problems, the optimal convergence is obtained. Numerical experiments are carried out to validate theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0252}, url = {http://global-sci.org/intro/article_detail/aamm/16931.html} }
TY - JOUR T1 - A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems AU - Wang , Nan AU - Chen , Jinru JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 879 EP - 901 PY - 2020 DA - 2020/06 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2018-0252 UR - https://global-sci.org/intro/article_detail/aamm/16931.html KW - Nonconforming extended finite element, Nitsche's method, elliptic interface problems, interface-unfitted mesh. AB -

This article proposes a new $P_{1}$ nonconforming Nitsche's extended finite element method for elliptic interface problems with interface-unfitted meshes. It is shown that the stability of the discrete formulation is independent of not only the mesh size and the diffusion parameters, but also the position of the interface, showing a robustness over the location of interface. In spite of the low regularity of interface problems, the optimal convergence is obtained. Numerical experiments are carried out to validate theoretical results.

Nan Wang & Jinru Chen. (2020). A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems. Advances in Applied Mathematics and Mechanics. 12 (4). 879-901. doi:10.4208/aamm.OA-2018-0252
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