Improved Error Estimation for the Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
Year: 2019
Author: Ruchi Guo, Tao Lin, Qiao Zhuang
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13015
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 4 : pp. 575–589
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Interface problems immersed finite element methods optimal convergence discontinuous coefficients finite element spaces interface independent mesh regularity.