Product integration-collocation methods for noncompact integral operator equations. (English) Zbl 0639.65074
This paper discusses the numerical solutions to a class of second-kind integral equations corresponding to the 2-D Laplace equation with corners on the boundary. The authors prove optimal orders of convergence of graded meshes based upon simple modifications on the underlying basis functions. Test examples point out that such modifications are of fundamental importance in some cases of polynomial collocation techniques.
Reviewer: J.C.F.Telles
MSC:
| 65R20 | Numerical methods for integral equations |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 45E05 | Integral equations with kernels of Cauchy type |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35C15 | Integral representations of solutions to PDEs |
Keywords:
second-kind integral equations; product integration; boundary integral equations; collocation; boundary element methods; Laplace equation; optimal orders of convergence; polynomial collocation techniquesReferences:
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