Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves

DOI10.1216/jiea/1181076016zbMath0899.65067OpenAlexW2025155618MaRDI QIDQ1386648

Kendall E. Atkinson, Ian H. Sloan

Publication date: 27 October 1998

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/nrm/vol93/cont9-3/cont9-3.htm

zbMATH Keywords

stabilityerror analysisLipschitz curvescollocationintegral equation methodsingular integral equationquadrature methodGalerkin methodssingle-layer equation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (2)

Galerkin approximation with quadrature for the screen problem in \(\mathbb{R}^3\) ⋮ Qualocation

Cites Work

• Spline qualocation methods for boundary integral equations
• A quadrature-based approach to improving the collocation method for splines of even degree
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• The convergence of spline collocation for strongly elliptic equations on curves
• The convergence of even degree spline collocation solution for potential problems in smooth domains of the plane
• A quadrature-based approach to improving the collocation method
• A Galerkin collocation method for some integral equations of the first kind
• Midpoint collocation for Cauchy singular integral equations
• Spline collocation for strongly elliptic equations on the torus
• Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\)
• On integral equations of the first kind with logarithmic kernels
• On the Asymptotic Convergence of Collocation Methods
• Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Error estimates for a discretized Galerkin method for a boundary integral equation in two dimensions
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