Volume 11, Issue 2
Numerical Analysis of Partially Penalized Immersed Finite Element Methods for Hyperbolic Interface Problems

Qing Yang

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 272-298.

Published online: 2018-11

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  • Abstract

We consider an approximation of second-order hyperbolic interface problems by partially penalized immersed finite element methods. In order to penalize the discontinuity of IFE functions, we add some stabilization terms at interface edges. Some semi-discrete and fully discrete schemes are presented and analyzed. We prove that the approximate solutions have optimal convergence rate in an energy norm. Numerical results not only validate the theoretical error estimates, but also indicate that our methods have smaller point-wise error over interface elements than classical IFE methods.

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@Article{NMTMA-11-272, author = {}, title = {Numerical Analysis of Partially Penalized Immersed Finite Element Methods for Hyperbolic Interface Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {272--298}, abstract = {

We consider an approximation of second-order hyperbolic interface problems by partially penalized immersed finite element methods. In order to penalize the discontinuity of IFE functions, we add some stabilization terms at interface edges. Some semi-discrete and fully discrete schemes are presented and analyzed. We prove that the approximate solutions have optimal convergence rate in an energy norm. Numerical results not only validate the theoretical error estimates, but also indicate that our methods have smaller point-wise error over interface elements than classical IFE methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0002}, url = {http://global-sci.org/intro/article_detail/nmtma/12430.html} }
TY - JOUR T1 - Numerical Analysis of Partially Penalized Immersed Finite Element Methods for Hyperbolic Interface Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 272 EP - 298 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0002 UR - https://global-sci.org/intro/article_detail/nmtma/12430.html KW - AB -

We consider an approximation of second-order hyperbolic interface problems by partially penalized immersed finite element methods. In order to penalize the discontinuity of IFE functions, we add some stabilization terms at interface edges. Some semi-discrete and fully discrete schemes are presented and analyzed. We prove that the approximate solutions have optimal convergence rate in an energy norm. Numerical results not only validate the theoretical error estimates, but also indicate that our methods have smaller point-wise error over interface elements than classical IFE methods.

Qing Yang. (2020). Numerical Analysis of Partially Penalized Immersed Finite Element Methods for Hyperbolic Interface Problems. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 272-298. doi:10.4208/nmtma.OA-2017-0002
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