Error analysis of boundary integral methods
- 1 January 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Acta Numerica
- Vol. 1, 287-339
- https://doi.org/10.1017/s0962492900002294
Abstract
Many of the boundary value problems traditionally cast as partial differential equations can be reformulated as integral equations over the boundary. After an introduction to boundary integral equations, this review describes some of the methods which have been proposed for their approximate solution. It discusses, as simply as possible, some of the techniques used in their error analysis, and points to areas in which the theory is still unsatisfactory.Keywords
This publication has 63 references indexed in Scilit:
- A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zeroIntegral Equations and Operator Theory, 1991
- Spline qualocation methods for boundary integral equationsNumerische Mathematik, 1990
- L p estimates of boundary integral equations for some nonlinear boundary value problemsNumerische Mathematik, 1990
- An Integral Equation Method for a Problem with Mixed Boundary ConditionsSIAM Journal on Mathematical Analysis, 1990
- The convergence of even degree spline collocation solution for potential problems in smooth domains of the planeNumerische Mathematik, 1988
- Boundary Integral Operators on Lipschitz Domains: Elementary ResultsSIAM Journal on Mathematical Analysis, 1988
- The convergence of spline collocation for strongly elliptic equations on curvesNumerische Mathematik, 1985
- Spectral properties of elliptic pseudodifferential operators on a closed curveFunctional Analysis and Its Applications, 1980
- Integralgleichungen erster Art und konforme AbbildungMathematische Zeitschrift, 1976
- Integral equation methods in potential theory. IProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1963