7 papers
A DPG method for Reissner-Mindlin plates
Thomas Führer, Norbert Heuer, Antti H. Niemi
We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation t…
MINRES for second-order PDEs with singular data
Thomas Führer, Norbert Heuer, Michael Karkulik
Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov--Galerkin method with optimal test functions (DPG) usually exclude singul…
A DPG method for shallow shells
Thomas Führer, Norbert Heuer, Antti H. Niemi
We develop and analyze a discontinuous Petrov--Galerkin method with optimal test functions (DPG method) for a shallow shell model of Koiter type. It is based on a uniformly stable…
Analysis of backward Euler primal DPG methods
Thomas Führer, Norbert Heuer, Michael Karkulik
We analyse backward Euler time stepping schemes for the primal DPG formulation of a class of parabolic problems. Optimal error estimates are shown in the natural norm and in the $L…
A robust DPG method for large domains
Thomas Führer, Norbert Heuer
We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincaré-type inequality. We show how robustness…
A locking-free DPG scheme for Timoshenko beams
Thomas Führer, Carlos García Vera, Norbert Heuer
We develop a discontinuous Petrov-Galerkin scheme with optimal test functions (DPG method) for the Timoshenko beam bending model with various boundary conditions, combining clamped…