4 papers
A fractional-order trace-dev-div inequality
Carsten Carstensen, Norbert Heuer
The trace-dev-div inequality in controls the trace in the norm of by that of the deviatoric part plus the norm of the divergence of a quadratic tensor field d…
Robust DPG Fortin operators
Thomas Führer, Norbert Heuer
At the fully discrete setting, stability of the discontinuous Petrov--Galerkin (DPG) method with optimal test functions requires local test spaces that ensure the existence of Fort…
A DPG method for the quad-curl problem
Thomas Führer, Pablo Herrera, Norbert Heuer
We derive an ultraweak variational formulation of the quad-curl problem in two and three dimensions. We present a discontinuous Petrov-Galerkin (DPG) method for its approximation a…
DPG methods for a fourth-order div problem
Thomas Führer, Pablo Herrera, Norbert Heuer
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and secon…