Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh‐refinement. Issue 6 (26th June 2013)

• Record Type: Journal Article
• Authors: Karkulik, Michael; Of, Günther; Praetorius, Dirk
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 6(2013:Nov.)
• Page Start: 2081
• Page End: 2106
• Publication Date: 2013-06-26
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21792
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We consider the adaptive lowest‐order boundary element method based on isotropic mesh refinement for the weakly‐singular integral equation for the three‐dimensional Laplacian. The proposed scheme resolves both, possible singularities of the solution as well as of the given data. The implementation thus only deals with discrete integral operators, that is, matrices. We prove that the usual adaptive mesh‐refining algorithm drives the corresponding error estimator to zero. Under an appropriate saturation assumption which is observed empirically, the sequence of discrete solutions thus tends to the exact solution within the energy norm. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>