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Volume 14, Issue 4-5
High Degree Immersed Finite Element Spaces by a Least Squares Method

Slimane Adjerid, Ruchi Guo & Tao Lin

Int. J. Numer. Anal. Mod., 14 (2017), pp. 604-626.

Published online: 2017-08

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  • Abstract

We present a least squares framework for constructing $p$-th degree immersed finite element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation enforces interface jump conditions including extended ones already proposed in the literature, and it guarantees the existence of $p$-th IFE shape functions on interface elements. The uniqueness of the proposed $p$-th degree IFE shape functions is also discussed. Computational results are presented to demonstrate the approximation capabilities of the proposed $p$-th IFE spaces as well as other features.

  • Keywords

Interface problems, discontinuous coefficients, finite element spaces, curved interfaces, higher order.

  • AMS Subject Headings

65N5, 65N30, 65N50, 35R05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-604, author = {Slimane Adjerid, Ruchi Guo and Tao Lin}, title = {High Degree Immersed Finite Element Spaces by a Least Squares Method}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {604--626}, abstract = {

We present a least squares framework for constructing $p$-th degree immersed finite element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation enforces interface jump conditions including extended ones already proposed in the literature, and it guarantees the existence of $p$-th IFE shape functions on interface elements. The uniqueness of the proposed $p$-th degree IFE shape functions is also discussed. Computational results are presented to demonstrate the approximation capabilities of the proposed $p$-th IFE spaces as well as other features.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10052.html} }
TY - JOUR T1 - High Degree Immersed Finite Element Spaces by a Least Squares Method AU - Slimane Adjerid, Ruchi Guo & Tao Lin JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 604 EP - 626 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10052.html KW - Interface problems, discontinuous coefficients, finite element spaces, curved interfaces, higher order. AB -

We present a least squares framework for constructing $p$-th degree immersed finite element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation enforces interface jump conditions including extended ones already proposed in the literature, and it guarantees the existence of $p$-th IFE shape functions on interface elements. The uniqueness of the proposed $p$-th degree IFE shape functions is also discussed. Computational results are presented to demonstrate the approximation capabilities of the proposed $p$-th IFE spaces as well as other features.

Slimane Adjerid, Ruchi Guo and Tao Lin. (2017). High Degree Immersed Finite Element Spaces by a Least Squares Method. International Journal of Numerical Analysis and Modeling. 14 (4-5). 604-626. doi:
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