Details
Original language | English |
---|---|
Title of host publication | Contemporary Computational Mathematics |
Subtitle of host publication | A Celebration of the 80th Birthday of Ian Sloan |
Publisher | Springer International Publishing AG |
Pages | 545-566 |
Number of pages | 22 |
ISBN (electronic) | 9783319724560 |
ISBN (print) | 9783319724553 |
Publication status | Published - 2018 |
Abstract
This paper is devoted to the approximate solution of a hypersingular integral equation on a closed polygonal boundary in ℝ2. We propose a fully discrete method with a trial space of trigonometric polynomials, combined with a trapezoidal rule approximation of the integrals. Before discretization the equation is transformed using a nonlinear (mesh grading) parametrization of the boundary curve which has the effect of smoothing out the singularities at the corners and yields fast convergence of the approximate solutions. The convergence results are illustrated with some numerical examples.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
Contemporary Computational Mathematics: A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG, 2018. p. 545-566.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - A discrete collocation method for a hypersingular integral equation on curves with corners
AU - Hartmann, Thomas
AU - Stephan, Ernst P.
N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018. All rights reserved.
PY - 2018
Y1 - 2018
N2 - This paper is devoted to the approximate solution of a hypersingular integral equation on a closed polygonal boundary in ℝ2. We propose a fully discrete method with a trial space of trigonometric polynomials, combined with a trapezoidal rule approximation of the integrals. Before discretization the equation is transformed using a nonlinear (mesh grading) parametrization of the boundary curve which has the effect of smoothing out the singularities at the corners and yields fast convergence of the approximate solutions. The convergence results are illustrated with some numerical examples.
AB - This paper is devoted to the approximate solution of a hypersingular integral equation on a closed polygonal boundary in ℝ2. We propose a fully discrete method with a trial space of trigonometric polynomials, combined with a trapezoidal rule approximation of the integrals. Before discretization the equation is transformed using a nonlinear (mesh grading) parametrization of the boundary curve which has the effect of smoothing out the singularities at the corners and yields fast convergence of the approximate solutions. The convergence results are illustrated with some numerical examples.
UR - http://www.scopus.com/inward/record.url?scp=85050487638&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-72456-0_25
DO - 10.1007/978-3-319-72456-0_25
M3 - Contribution to book/anthology
AN - SCOPUS:85050487638
SN - 9783319724553
SP - 545
EP - 566
BT - Contemporary Computational Mathematics
PB - Springer International Publishing AG
ER -