Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity
Date
2012ISSN
0749159XSource
Numerical Methods for Partial Differential EquationsVolume
28Issue
3Pages
749767Google Scholar check
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In this article, we analyze the singular function boundary integral method (SFBIM) for a twodimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stickslip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution, and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. By means of Green's theorem, the resulting discretized equations are posed and solved on the boundary of the domain, away from the point where the singularity arises. We analyze the convergence of the method and prove that the coefficients in the local asymptotic expansion, also referred to as stress intensity factors, are approximated at an exponential rate as the number of the employed expansion terms is increased. Our theoretical results are illustrated through a numerical experiment. Copyright © 2011 Wiley Periodicals, Inc.
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