Error analysis of a boundary element collocation method for a screen problem in ${\bf R}\sp 3$
Open Access
- 1 May 1992
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 58 (198) , 575
- https://doi.org/10.1090/s0025-5718-1992-1122060-9
Abstract
We examine the numerical approximation of the first-kind integral equation on a plane rectangle defined by the single-layer potential of the three-dimensional Laplacian. The solution is approximated by nodal collocation with piecewise bilinear trial functions on a rectangular grid. We prove stability and convergence of this method in the Sobolev space . A key ingredient in the proof is the observation that the collocation equations define symmetric positive definite Toeplitz matrices.Keywords
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