Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 30, Issue 3, Pages 870-885Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drn081
Keywords
interface problem; non-matching grids; edge stabilization
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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.
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