Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems
Journal article, 2010

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.

non-matching grids

interface problem

edge stabilization

Author

Erik Burman

Ecole Polytechnique Federale De Lausanne

Peter F G Hansbo

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. 30 3 870-885

Subject Categories

Computational Mathematics

DOI

10.1093/imanum/drn081

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5/3/2018 1