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Improved impedance conditions for a thin layer problem in a nonsmooth domain
Author(s) -
Auvray Alexis,
Vial Grégory
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5434
Subject(s) - mathematics , electrical impedance , mathematical analysis , gravitational singularity , laplace transform , domain (mathematical analysis) , boundary value problem , laplace's equation , boundary layer , thin layer , layer (electronics) , mechanics , materials science , physics , composite material , quantum mechanics
In this article, we consider the model problem of the Laplace equation in a domain with a thin layer on a part of its boundary. The singularities appearing where boundary conditions change deteriorate the efficiency of the classical impedance condition used to replace the layer. Modified impedance conditions are proposed, which lead to some improvements in the error estimates.