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Error estimates for a discretized Galerkin method for a boundary integral equation in two dimensions
Author(s) -
Penzel F.
Publication year - 1992
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690080502
Subject(s) - mathematics , piecewise , galerkin method , discretization , a priori and a posteriori , mathematical analysis , convergence (economics) , numerical integration , finite element method , boundary (topology) , constant (computer programming) , integral equation , square (algebra) , a priori estimate , geometry , computer science , philosophy , physics , epistemology , economics , thermodynamics , programming language , economic growth
We present a priori and a posteriori 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. © 1992 John Wiley & Sons, Inc.