ULTRA-WEAK FORMULATION OF A HYPERSINGULAR INTEGRAL EQUATION ON POLYGONS AND DPG METHOD WITH OPTIMAL TEST FUNCTIONS

摘要

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 with uniform and adaptively refined meshes.