Discontinuous bubble scheme for elliptic problems with jumps in the solution

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We propose a new numerical method to solve an elliptic problem with jumps both in the solution and derivative along an interface. By considering a suitable function which has the same jumps as the solution, we transform the problem into one without jumps. Then we apply the immersed finite element method in which we allow uniform meshes so that the interface may cut through elements to discretize the problem as introduced in [1-3]. Some convenient way of approximating the jumps of the solution by piecewise linear functions is suggested. Our method can also handle the case when the interface passes through grid points. We believe this paper presents the first resolution of such cases. Numerical experiments for various problems show second-order convergence in L(2) and first order in H(1)-norms. Moreover, the convergence order is very robust for all problems tested. (C) 2010 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE SA
Issue Date
2011
Language
English
Article Type
Article
Keywords

IMMERSED INTERFACE METHOD; FINITE-ELEMENT SPACE; APPROXIMATION CAPABILITY; EQUATIONS; FLOW; ELECTROPORATION; COEFFICIENTS

Citation

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v.200, no.5-8, pp.494 - 508

ISSN
0045-7825
DOI
10.1016/j.cma.2010.06.029
URI
http://hdl.handle.net/10203/20243
Appears in Collection
MA-Journal Papers(저널논문)
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