THE BOUNDARY INTEGRAL METHOD FOR THE LAPLACE EQUATION WITH MIXED AND OBLIQUE CONDITIONS
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The solvability of the mixed and oblique boundary value problem is established by the Boundary Integral Equation method. Based on the Green formula, we express the solution in terms of the bound-ary data. The key to the realization of this method is to translate the tangential derivative to the fundamental solution. A system of bound-ary integral equation of second kind Fredholm type is obtained. By the Fredholm and Riez theorem, the existence and the uniqueness of the solution is established.
Abstract
The solvability of the mixed and oblique boundary value problem is established by the Boundary Integral Equation method. Based on the Green formula, we express the solution in terms of the bound-ary data. The key to the realization of this method is to translate the tangential derivative to the fundamental solution. A system of bound-ary integral equation of second kind Fredholm type is obtained. By the Fredholm and Riez theorem, the existence and the uniqueness of the solution is established.
참고문헌 (11)
- A.K. Aziz, "Mathematical foundation of the finite element method with applications to partial differential equation", Academic press
- M.Costabel, "boundary integral equations for mixed boundary value problems in polygonaldomain and Galerkine approximation" (1985), Banach center publication
- M.Costabel, "Strong ellipticity of boundary integral operators", J. Reine Angew. Math, 372, pp.39~63 (1986)
- J.Giroire, "Numerical solution of exterior Neumann problem using a double layer potentiel", Math.Comp, 32 (1968)
- J.Kohn, "On the algebra of pseudo differential operators", Comm.Pure Appl.Math, 18 (1968)
- V.A.Kozlov, "Elliptic value problems in domains with point singularities", Mathematical surveys and Monographs, A.M.S, 52 (1997)
- G.Hsiao, "Boundary integral equations", App. Math.Sciences, 164 (2008), Springer
- J.Treve, "Introduction to pseudodifferential and fourier integral operators" (1964), Plenom press
- C.A. Brebbia, "Boundary Element Techniques" (1984), Springer
- D.Lesnic, "The boundary Element method for solving the Laplace equation in two dimensions with oblique derivative boundary conditions", Communications in numerical methods in engineering, 23, pp.1071~1080 (2007)
- W.L. Wendland, "On the integral equation method for the plane mixed boundary value problem of Laplacian", Math. Method Appl. Sci, 1, pp.265~321 (1979)