Resolution of a long-standing open question in the numerical analysis of boundary integral equations for Laplace's equation

Abstract: 

Today they are used extensively in applied maths and industry to compute approximations of the solutions to Laplace's equation (and other PDEs), with many numerical schemes based on the Galerkin method.

Perhaps surprisingly, however, it has not yet been proved whether or not the Galerkin method converges when applied to the standard second-kind boundary integral equations for Laplace's equation on general Lipschitz domains, or even general 3-d Lipschitz polyhedra.

In this talk, I will describe recent results obtained with Simon Chandler-Wilde (University of Reading) that settle this convergence question.