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 H2 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 H3 regularity was assumed. Furthermore, with the standard piecewise H2 regularity assumption, this paper proves that these PPIFE methods also converge optimally in the L2 norm which could not be proved in [25] because of the excessive H3 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.