%0 Journal Article
%T Ultra-weak formulation of a hypersingular integral equation on polygons and DPG method with optimal test functions
%A Norbert Heuer
%A Felipe Pinochet
%J Mathematics
%D 2013
%I arXiv
%X We present an ultra-weak formulation of a hypersingular integral equation on closed polygons and prove its well-posedness and equivalence with the standard variational formulation. Based on this ultra-weak formulation we present a discontinuous Petrov-Galerkin method with optimal test functions and prove its quasi-optimal convergence in $L^2$. Theoretical results are confirmed by numerical experiments on an open curve with uniform and adaptively refined meshes.
%U http://arxiv.org/abs/1309.1697v1