TY - JOUR

T1 - Small obstacle asymptotics for a 2D semi-linear convex problem

AU - Claeys, X.

AU - Chesnel, L.

AU - Nazarov, S.A.

PY - 2018/4/26

Y1 - 2018/4/26

N2 - We study a 2D semi-linear equation in a domain with a small Dirichlet obstacle of size δ > 0. 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.

AB - We study a 2D semi-linear equation in a domain with a small Dirichlet obstacle of size δ > 0. 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.

KW - Small obstacle

KW - asymptotic analysis

KW - semi-linear convex problem

KW - singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=85014494070&partnerID=8YFLogxK

U2 - 10.1080/00036811.2017.1295449

DO - 10.1080/00036811.2017.1295449

M3 - Article

VL - 97

SP - 962

EP - 981

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 6

ER -