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Article Dans Une Revue Applicable Analysis Année : 2017

Small obstacle asymptotics for a 2D semi-linear convex problem

Résumé

We study a 2D semi-linear equation in a domain with a small Dirichlet obstacle of size δ. Using the method of matched asymptotic expansions, we compute an asymptotic expansion of the solution as δ tends to zero. Its relevance is justified by proving a rigorous error estimate. Then we construct an approximate model, based on an equation set in the limit domain without the small obstacle, which provides a good approximation of the far field of the solution of the original problem. The interest of this approximate model lies in the fact that it leads to a variational formulation which is very simple to discretize. We present numerical experiments to illustrate the analysis.
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Dates et versions

hal-01427617 , version 1 (05-01-2017)

Identifiants

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Lucas Chesnel, Xavier Claeys, Sergei A Nazarov. Small obstacle asymptotics for a 2D semi-linear convex problem. Applicable Analysis, 2017, pp.20. ⟨10.1080/00036811.2017.1295449⟩. ⟨hal-01427617⟩
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