Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation
Martin Costabel, Ernst Stephan (1985)
Banach Center Publications
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Martin Costabel, Ernst Stephan (1985)
Banach Center Publications
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Ján Filo, Stephan Luckhaus (2000)
Journal of the European Mathematical Society
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An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try to present a general framework where deterministic homogenization methods can be applied to calculate the second term in the asymptotic expansion with respect to the small parameter characterizing the oscillations.
J. B. Díaz, R. B. Ram (1979)
Collectanea Mathematica
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T. KIYONO, M. SHIMASAKI (1970/71)
Numerische Mathematik
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D. Radunović (1986)
Matematički Vesnik
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P. HOFMANN (1966/67)
Numerische Mathematik
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Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed,...
Currie, Sonja, Love, Anne D. (2010)
Advances in Difference Equations [electronic only]
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R. Bunoiu, G. Cardone, S. A. Nazarov (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, the relative...
Ta Van Dinh (1987)
Aplikace matematiky
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The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the...
Dagmar Medková (2008)
Applicationes Mathematicae
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The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
Zayed, E.M.E. (1991)
International Journal of Mathematics and Mathematical Sciences
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