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Volume 16, Issue 4
Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems

Ruchi Guo, Tao Lin & Qiao Zhuang

Int. J. Numer. Anal. Mod., 16 (2019), pp. 575-589.

Published online: 2019-02

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  • Abstract

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise $H$2 regularity assumption for the exact solution. In energy norms, the error estimates given in this paper are better than those in [25] where a stronger piecewise $H$3 regularity was assumed. Furthermore, with the standard piecewise $H$2 regularity assumption, this paper proves that these PPIFE methods also converge optimally in the $L$2 norm which could not be proved in [25] because of the excessive $H$3 regularity requirement.

  • Keywords

Interface problems, immersed finite element methods, optimal convergence, discontinuous coefficients, finite element spaces, interface independent mesh, regularity.

  • AMS Subject Headings

35R35, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ruchi91@vt.edu (Ruchi Guo)

tlin@vt.edu (Tao Lin)

qzhuang@vt.edu (Qiao Zhuang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-575, author = {Guo , RuchiLin , Tao and Zhuang , Qiao}, title = {Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {4}, pages = {575--589}, abstract = {

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise $H$2 regularity assumption for the exact solution. In energy norms, the error estimates given in this paper are better than those in [25] where a stronger piecewise $H$3 regularity was assumed. Furthermore, with the standard piecewise $H$2 regularity assumption, this paper proves that these PPIFE methods also converge optimally in the $L$2 norm which could not be proved in [25] because of the excessive $H$3 regularity requirement.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13015.html} }
TY - JOUR T1 - Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems AU - Guo , Ruchi AU - Lin , Tao AU - Zhuang , Qiao JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 575 EP - 589 PY - 2019 DA - 2019/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13015.html KW - Interface problems, immersed finite element methods, optimal convergence, discontinuous coefficients, finite element spaces, interface independent mesh, regularity. AB -

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise $H$2 regularity assumption for the exact solution. In energy norms, the error estimates given in this paper are better than those in [25] where a stronger piecewise $H$3 regularity was assumed. Furthermore, with the standard piecewise $H$2 regularity assumption, this paper proves that these PPIFE methods also converge optimally in the $L$2 norm which could not be proved in [25] because of the excessive $H$3 regularity requirement.

Guo , RuchiLin , Tao and Zhuang , Qiao. (2019). Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems. International Journal of Numerical Analysis and Modeling. 16 (4). 575-589. doi:
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