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

F. Lefevre, S. Lohrengel & S. Nicaise

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, domains with cracks, XFEM, 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 and S. Nicaise. (2011). 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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