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Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems
Daniel Jodlbauer, Ulrich Langer, Thomas Wick +1
We consider the widely used continuous - quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes an…
Space-time hexahedral finite element methods for parabolic evolution problems
Ulrich Langer, Andreas Schafelner
We present locally stabilized, conforming space-time finite element methods for parabolic evolution equations on hexahedral decompositions of the space-time cylinder. Tensor-produc…
Simultaneous space-time finite element methods for parabolic optimal control problems
Ulrich Langer, Andreas Schafelner
This work presents, analyzes and tests stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time trac…
Robust discretization and solvers for elliptic optimal control problems with energy regularization
Ulrich Langer, Olaf Steinbach, Huidong Yang
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. T…
Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces
Ulrich Langer, Marco Zank
We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This…
Parallel matrix-free higher-order finite element solvers for phase-field fracture problems
Daniel Jodlbauer, Ulrich Langer, Thomas Wick
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with…