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An integral equation approximation of the mixed problem for the laplacian in R 3
Author(s) -
Baldino R. R.,
Nedelec J. C.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030132
Subject(s) - mathematics , bounded function , mathematical analysis , singularity , bilinear interpolation , simple (philosophy) , bilinear form , pure mathematics , philosophy , statistics , epistemology
An integral representation for the solutions of the interior and exterior homogeneous mixed problems on a regular bounded open set in R 3 is given in terms of a potential of simple layer on the Dirichlet data and of double layer on the Neumann data. A coercive non‐symmetric bilinear form is provided. Singular finite elements containing the first terms of the assymptotic expansion of the singularity are built and error estimates for the surface distributions are given.