Quadrature methods for 2D and 3D problems
The paper gives an overview on well-known stability and convergence results for simple quadrature methods based on low-order composite quadrature rules and applied to the numerical solution of integral equations over smooth manifolds. The methods for the case of second-kind equations are explained, and what is known for the analysis of pseudodifferentlal equations is discussed. These simple methods are not recommended for integral equations over domains with dimension higher than one. For the solution of a two-dimensional singular integral equation, a new result on a quadrature method based on product rules is proved. The paper is clearly and carefully written, presenting many detailed investigations; there are 60 essential references. It will be of great interest to numerical analysts working with solution methods for integral equations.
integral equations over smooth manifolds
scientific article; zbMATH DE number 1566028
scientific article