Abstract
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.
Full Text
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call