Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 153-190 |
| Seitenumfang | 38 |
| Fachzeitschrift | Numerische Mathematik |
| Jahrgang | 140 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 19 März 2018 |
| Publikationsstatus | Veröffentlicht - Sept. 2018 |
Abstract
We consider the direct boundary integral equation formulation for the mixed Dirichlet–Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and trigonometric polynomials. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. Special care is taken for handling the hypersingular operator as in Hartmann and Stephan (in: Dick, Kuo, Wozniakowski (eds) Festschrift for the 80th birthday of Ian Sloan, Springer, Berlin, 2018). With the indirect method used in Elschner et al. (Numer Math 76(3):355–381, 1997) this was avoided. Using Mellin transformation techniques a stability and solvability analysis of the transformed integral equations can be performed, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Numerische Mathematik, Jahrgang 140, Nr. 1, 09.2018, S. 153-190.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Collocation with trigonometric polynomials for integral equations to the mixed boundary value problem
AU - Stephan, Ernst P.
AU - Teltscher, Matthias T.
N1 - Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/9
Y1 - 2018/9
N2 - We consider the direct boundary integral equation formulation for the mixed Dirichlet–Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and trigonometric polynomials. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. Special care is taken for handling the hypersingular operator as in Hartmann and Stephan (in: Dick, Kuo, Wozniakowski (eds) Festschrift for the 80th birthday of Ian Sloan, Springer, Berlin, 2018). With the indirect method used in Elschner et al. (Numer Math 76(3):355–381, 1997) this was avoided. Using Mellin transformation techniques a stability and solvability analysis of the transformed integral equations can be performed, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space.
AB - We consider the direct boundary integral equation formulation for the mixed Dirichlet–Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and trigonometric polynomials. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. Special care is taken for handling the hypersingular operator as in Hartmann and Stephan (in: Dick, Kuo, Wozniakowski (eds) Festschrift for the 80th birthday of Ian Sloan, Springer, Berlin, 2018). With the indirect method used in Elschner et al. (Numer Math 76(3):355–381, 1997) this was avoided. Using Mellin transformation techniques a stability and solvability analysis of the transformed integral equations can be performed, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space.
UR - http://www.scopus.com/inward/record.url?scp=85044198297&partnerID=8YFLogxK
U2 - 10.1007/s00211-018-0960-8
DO - 10.1007/s00211-018-0960-8
M3 - Article
AN - SCOPUS:85044198297
VL - 140
SP - 153
EP - 190
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1
ER -