Error estimates for a discretized Galerkin method for a boundary integral equation in two dimensions

Abstract

We present a priori and a posferiori estimates for the error between the Galerkin and a discretized Galerkin method for the boundary integral equation for the single layer potential on the square plate. Using piecewise constant finite elements on a rectangular mesh we study the error coming from numerical integration. The crucial point of our analysis is the estimation of some error constants, and we demonstrate that this is necessary if our methods are to be used. After the determination of these constants we are in the position to prove invertibility and quasioptimal convergence results for our numerical scheme, if the chosen numerical integration formulas are sufficiently precise. 0 1992 John Wiley & Sons, Inc.

Gemischte Fourier‐Randelementmethoden zur Berechnung zeitharmonischer Streufelder an Schirmen

“…Zusammenfassend laRt sich feststellen, daR das hier beschriebene Verfahren im vorliegenden Fall (Abschnitt 7) schnell zu guten Ergebnissen fuhrt (fur kleine Wellenzahlen), eine zuverlassige Abschatzung der numerisch erzielten Konvergenzraten erfordert jedoch die Betrachtung der Frage, in wieweit die Diskretisierung der Integrale einen EinfluR auf die Rechnungen haben. Dies ist eine Fragestellung, deren Beantwortung wohl zahlreiche Fehlerabschatzungen wie sie in [51] durchgefuhrt wurden, erfordert.…”

Convergence of boundary element collocation methods for dirichlet and neumann screen problems in R3

“…Therefore the convergence of any Downloaded by [Michigan State University] at 21:35 08 February 2015 Galerkin approximation scheme for (1.1) and (1.2) in the Hilbert spaces mentioned above, is well known. Such Galerkin schemes with various spline spaces have been studied theoretically as well as practically by several authors (see [27], [17], [9], [lo], [ W ) .…”

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Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations

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