3 papers
math.NA2021
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…
math.NA2021
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…
math.NA2019
Space-time least-squares finite elements for parabolic equations
Thomas Führer, Michael Karkulik
We present a space-time least squares finite element method for the heat equation. It is based on residual minimization in L2 norms in space-time of an equivalent first order syste…