IJPAM: Volume 104, No. 3 (2015)


Do Y. Kwak$^1$, Juho Lee$^2$
$^{1,2}$Department of Mathematical Sciences
KAIST, 291 Daehak-ro, Yuseong-gu
Daejeon, 305-701, KOREA

Abstract. In recent years, the immersed finite element methods (IFEM) introduced in [20], [21] to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of researchers because of their simplicity and efficiency. Unlike the conventional finite element methods, the IFEM allows the interface to cut through the interior of the element, yet after the basis functions are altered so that they satisfy the flux jump conditions, it seems to show a reasonable order of convergence.

In this paper, we propose an improved version of the $P_1$ based IFEM by adding the line integral of flux terms on each element. This technique resembles the discontinuous Galerkin (DG) method, however, our method has much less degrees of freedom than the DG methods since we use the same number of unknowns as the conventional $P_1$ finite element method.

We prove $H^1$ and $L^2$ error estimates which are optimal both in order and regularity. Numerical experiments were carried out for several examples, which show the robustness of our scheme.

Received: August 24, 2015

AMS Subject Classification: 65N30, 74S05, 76S05

Key Words and Phrases: modified $P_1$-immersed finite element, flux jump, discontinuous Galerkin, NIPG, SIPG

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DOI: 10.12732/ijpam.v104i3.14 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 471 - 494

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