Convergence Analysis of Nitsche Extended Finite Element Methods for H(Curl)-Elliptic Interface Problems
Year: 2022
Author: Nan Wang, Jinru Chen
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20656
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 4 : pp. 487–510
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Nitsche extended finite element method H(curl)-elliptic interface problems interface-unfitted meshes the lowest order of second family Nédélec edge elements.