76 citations · 315 across the 31 of their papers we have counts for
45 papers
Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions
Thomas Führer, Gregor Gantner, Roberto González +1
We construct Scott-Zhang-type space-time quasi-interpolation operators on tensor- product meshes for parabolic settings. Specifically, these are linear and uniformly bounded projec…
Adaptive finite element methods with optimally preconditioned GMRES guarantee optimal complexity
Thomas Führer, Paula Hilbert, Ani Miraçi +1
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting.…
A posteriori analysis of neural network approximations
Thomas Führer, Sergio Rojas
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily g…
Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs
Thomas Führer, Gregor Gantner
We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, whi…
Quasi-interpolators with application to postprocessing in finite element methods
Thomas Führer, Manuel A. Sánchez
We design quasi-interpolation operators based on piecewise polynomial weight functions of degree less than or equal to that map into the space of continuous piecewise polynomia…
Robust hybrid finite element methods for reaction-dominated diffusion problems
Thomas Führer, Diego Paredes
For a reaction-dominated diffusion problem we study a primal and a dual hybrid finite element method where weak continuity conditions are enforced by Lagrange multipliers. Uniform…
Well-posedness of first-order acoustic wave equations and space-time finite element approximation
Thomas Führer, Roberto González, Michael Karkulik
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to…
A DPG method for linear quadratic optimal control problems
Thomas Führer, Francisco Fuica
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solutio…
Mixed finite elements for Kirchhoff-Love plate bending
Thomas Führer, Norbert Heuer
We present a mixed finite element method with triangular and parallelogram meshes for the Kirchhoff-Love plate bending model. Critical ingredient is the construction of low-dimensi…
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…
Least-squares finite elements for distributed optimal control problems
Thomas Führer, Michael Karkulik
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously so…
On a mixed FEM and a FOSLS with loads
Thomas Führer
We study variants of the mixed finite element method (mixed FEM) and the first-order system least-squares finite element (FOSLS) for the Poisson problem where we replace the load b…
Space-time finite element methods for parabolic distributed optimal control problems
Thomas Führer, Michael Karkulik
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order o…
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…
Multilevel decompositions and norms for negative order Sobolev spaces
Thomas Führer
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in for . Proofs are given in the case of uniformly and locall…
Trace operators of the bi-Laplacian and applications
Thomas Führer, Alexander Haberl, Norbert Heuer
We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with h…
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
Thomas Führer, Gregor Gantner, Dirk Praetorius +1
We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular…
Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two
Thomas Führer, Norbert Heuer
We present quasi-diagonal preconditioners for piecewise polynomial discretizations of pseudodifferential operators of order minus two in any space dimension. Here, quasi-diagonal m…
Adaptive BEM with inexact PCG solver yields almost optimal computational costs
Thomas Führer, Alexander Haberl, Dirk Praetorius +1
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equati…
Fully discrete DPG methods for the Kirchhoff-Love plate bending model
Thomas Führer, Norbert Heuer
We extend the analysis and discretization of the Kirchhoff-Love plate bending problem from [T. Führer, N. Heuer, A.H. Niemi, An ultraweak formulation of the Kirchhoff-Love plate be…
An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation
Thomas Führer, Norbert Heuer, Antti H. Niemi
We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff-Love plate bending model. Based on this formulation, we introduce a discretization of the…
New a priori analysis of first-order system least-squares finite element methods for parabolic problems
Thomas Führer, Michael Karkulik
We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of th…
First-Order Least-Squares Method for the Obstacle Problem
Thomas Führer
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on…