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Interior-penalty-stabilized Lagrange multiplier methods for the finite-element solution of elliptic interface problems
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posted on 2023-06-08, 05:00 authored by Erik Burman, Peter HansboIn 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.
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Publication status
- Published
Journal
IMA Journal of Numerical AnalysisISSN
0272-4979External DOI
Issue
3Volume
30Page range
870-885Pages
16.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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