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

DOI:

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

Published online: 1970-01

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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 H2regularity 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 H3regularity was assumed. Furthermore, with the standard piecewise H2regularity 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 H3regularity 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)

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