The convergence of a direct BEM for the plane mixed boundary value problem of the Laplacian. (English) Zbl 0661.65116
The authors achieve a convergence analysis of a collocation method proposed to solve a mixed (Dirichlet and Neumann) boundary value problem for the Laplace equation in a smooth plane domain. They emphasize that up to that moment convergence results for collocation procedures with piecewise polynomial trial functions were available only in the cases when either the part of contour of domain with Dirichlet condition or the part of contour with Neumann condition vanishes. Some numerical examples are exposed.
Reviewer: C.-I.Gheorghiu
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65R20 | Numerical methods for integral equations |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 45F15 | Systems of singular linear integral equations |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
mixed boundary conditions; asymptotic error estimates; boundary element method; convergence; collocation method; Laplace equation; numerical examplesReferences:
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