Volume 8, Issue 4
An Extended Finite Element Method for 2D Edge Elements

F. Lefevre, S. Lohrengel & S. Nicaise

DOI:

Int. J. Numer. Anal. Mod., 8 (2011), pp. 641-666

Published online: 2011-08

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  • Abstract

A new eXtended Finite Element Method based on two-dimensional edge elements is presented and applied to solve the time-harmonic Maxwell equations in domains with cracks. Error analysis is performed and shows the method to be convergent with an order of at least $O(h^{1/2-\eta})$. The implementation of the method is discussed and numerical tests illustrate its performance.

  • Keywords

Maxwell's equations domains with cracks XFEM singularities of solutions

  • AMS Subject Headings

65N30 65N15 78M10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-641, author = {F. Lefevre, S. Lohrengel and S. Nicaise}, title = {An Extended Finite Element Method for 2D Edge Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {4}, pages = {641--666}, abstract = {A new eXtended Finite Element Method based on two-dimensional edge elements is presented and applied to solve the time-harmonic Maxwell equations in domains with cracks. Error analysis is performed and shows the method to be convergent with an order of at least $O(h^{1/2-\eta})$. The implementation of the method is discussed and numerical tests illustrate its performance.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/705.html} }
TY - JOUR T1 - An Extended Finite Element Method for 2D Edge Elements AU - F. Lefevre, S. Lohrengel & S. Nicaise JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 641 EP - 666 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/705.html KW - Maxwell's equations KW - domains with cracks KW - XFEM KW - singularities of solutions AB - A new eXtended Finite Element Method based on two-dimensional edge elements is presented and applied to solve the time-harmonic Maxwell equations in domains with cracks. Error analysis is performed and shows the method to be convergent with an order of at least $O(h^{1/2-\eta})$. The implementation of the method is discussed and numerical tests illustrate its performance.
F. Lefevre, S. Lohrengel & S. Nicaise. (1970). An Extended Finite Element Method for 2D Edge Elements. International Journal of Numerical Analysis and Modeling. 8 (4). 641-666. doi:
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