97 citations · 381 across the 25 of their papers we have counts for
5 papers · 1 filter
DPG method with optimal test functions for a transmission problem
Norbert Heuer, Michael Karkulik
We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary inte…
Local high-order regularization and applications to hp-methods
Michael Karkulik, Jens Markus Melenk
We develop a regularization operator based on smoothing on a locally defined length scale. This operator is defined on and has approximation properties that are given by the…
Discontinuous Petrov-Galerkin boundary elements
Norbert Heuer, Michael Karkulik
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Nu…
Note on discontinuous trace approximation in the practical DPG method
Norbert Heuer, Michael Karkulik, Francisco-Javier Sayas
We analyze a non-conforming DPG method with discontinuous trace approximation for the Poisson problem in two and three space dimensions. We show its well-posedness and quasi-optima…
Adaptive Boundary Element Methods
Michael Feischl, Thomas Führer, Norbert Heuer +2
This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of availabl…