Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems

Burman, Erik and Hansbo, Peter (2010) Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems. IMA Journal of Numerical Analysis, 30 (3). pp. 870-885. ISSN 0272-4979

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Abstract

In this paper we propose a class of jump-stabilized Lagrange multiplier methods for the finite-element solution of multidomain elliptic partial differential equations using piecewise-constant or continuous piecewise-linear approximations of the multipliers. For the purpose of stabilization we use the jumps in derivatives of the multipliers or, for piecewise constants, the jump in the multipliers themselves, across element borders. The ideas are illustrated using Poisson's equation as a model, and the proposed method is shown to be stable and optimally convergent. Numerical experiments demonstrating the theoretical results are also presented.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:06
Last Modified: 04 Apr 2012 11:51
URI: http://sro.sussex.ac.uk/id/eprint/24070
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