Error analysis of a boundary element collocation method for a screen problem in 𝑅³

Costabel, M.; Penzel, F.; Schneider, R.

doi:10.1090/S0025-5718-1992-1122060-9

Error analysis of a boundary element collocation method for a screen problem in $\textbf {R}^ 3$
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by M. Costabel, F. Penzel and R. Schneider PDF

Math. Comp. 58 (1992), 575-586 Request permission

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 ${\tilde H^{ - 1/2}}$. A key ingredient in the proof is the observation that the collocation equations define symmetric positive definite Toeplitz matrices.

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