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Volume 19, Issue 4
Convergence Analysis of Nitsche Extended Finite Element Methods for H(Curl)-Elliptic Interface Problems

Nan Wang & Jinru Chen

Int. J. Numer. Anal. Mod., 19 (2022), pp. 487-510.

Published online: 2022-06

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  • Abstract

An H(curl)-conforming Nitsche extended finite element method is proposed for H(curl)-elliptic interface problems in three dimensional Lipschitz domains with smooth interfaces. Under interface-unfitted meshes, the continuous problems are discretized by an H(curl)-conforming extended finite element space, which is constructed based on the the lowest order of second family Nédélec edge elements (Whitney elements). A stabilization term defined on transmission faces is added to the standard discrete bilinear form. Stability results and the optimal error estimate in the parameter-dependent H(curl)-norm are derived, which are both uniform with respect to not only the mesh size and the interface position but also the physical parameters. Numerical experiments are carried out to validate theoretical results.

  • Keywords

Nitsche extended finite element method, H(curl)-elliptic interface problems, interface-unfitted meshes, the lowest order of second family Nédélec edge elements.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-487, author = {Wang , Nan and Chen , Jinru}, title = {Convergence Analysis of Nitsche Extended Finite Element Methods for H(Curl)-Elliptic Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {4}, pages = {487--510}, abstract = {

An H(curl)-conforming Nitsche extended finite element method is proposed for H(curl)-elliptic interface problems in three dimensional Lipschitz domains with smooth interfaces. Under interface-unfitted meshes, the continuous problems are discretized by an H(curl)-conforming extended finite element space, which is constructed based on the the lowest order of second family Nédélec edge elements (Whitney elements). A stabilization term defined on transmission faces is added to the standard discrete bilinear form. Stability results and the optimal error estimate in the parameter-dependent H(curl)-norm are derived, which are both uniform with respect to not only the mesh size and the interface position but also the physical parameters. Numerical experiments are carried out to validate theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20656.html} }
TY - JOUR T1 - Convergence Analysis of Nitsche Extended Finite Element Methods for H(Curl)-Elliptic Interface Problems AU - Wang , Nan AU - Chen , Jinru JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 487 EP - 510 PY - 2022 DA - 2022/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20656.html KW - Nitsche extended finite element method, H(curl)-elliptic interface problems, interface-unfitted meshes, the lowest order of second family Nédélec edge elements. AB -

An H(curl)-conforming Nitsche extended finite element method is proposed for H(curl)-elliptic interface problems in three dimensional Lipschitz domains with smooth interfaces. Under interface-unfitted meshes, the continuous problems are discretized by an H(curl)-conforming extended finite element space, which is constructed based on the the lowest order of second family Nédélec edge elements (Whitney elements). A stabilization term defined on transmission faces is added to the standard discrete bilinear form. Stability results and the optimal error estimate in the parameter-dependent H(curl)-norm are derived, which are both uniform with respect to not only the mesh size and the interface position but also the physical parameters. Numerical experiments are carried out to validate theoretical results.

Wang , Nan and Chen , Jinru. (2022). Convergence Analysis of Nitsche Extended Finite Element Methods for H(Curl)-Elliptic Interface Problems. International Journal of Numerical Analysis and Modeling. 19 (4). 487-510. doi:
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