Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems

Tao Lin; Yanping Lin; Weiwei Sun

doi:10.3934/dcdsb.2007.7.807

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2007, Volume 7, Issue 4: 807-823. Doi: 10.3934/dcdsb.2007.7.807

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Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems

1.
Department of Mathematics, Virginia Tech, Blackburg, VA, 24061-0123
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, Canada T6G 2G1
3.
Department of Mathematics, City University of Hong Kong, Koloon Tong, Hong Kong

Received: September 30, 2006

Revised: January 31, 2007

Published: October 2007

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Abstract

We carry out error estimation of a class of immersed finite element (IFE) methods for elliptic interface problems with both perfect and imperfect interface jump conditions. A key feature of these methods is that their partitions can be independent of the location of the interface. These quadratic IFE spaces reduce to the standard quadratic finite element space when the interface is not in the interior of any element. More importantly, we demonstrate that these IFE spaces have the optimal (slightly lower order in one case) approximation capability expected from a finite element space using quadratic polynomials.

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Mathematics Subject Classification: 90A09, 65K10, 65M12, 65M60.

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