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Numerical approximation of a singularly perturbed contact problem. (English) Zbl 0955.74048
Summary: As a simplified model for contact problems, we study a mixed Neumann-Robin boundary value problem for the Laplace operator in a smooth domain in \(\mathbb{R}^2\). The Robin condition contains a small parameter \(\varepsilon\) inducing boundary layers of corner type at the transition points. We present an integral equation for the numerical solution of this problem together with estimates of the error. We also investigate an improvement obtained if we add to the discrete space some special functions.

MSC:
74M15 Contact in solid mechanics
74S15 Boundary element methods applied to problems in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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