39 citations · 114 across the 35 of their papers we have counts for
51 papers
Generalized mixed and primal hybrid methods with applications to plate bending
Norbert Heuer
We present an extended framework for hybrid finite element approximations of self-adjoint, positive definite operators. It covers the cases of primal, mixed, and ultraweak formulat…
A balanced finite-element method for an axisymmetrically loaded thin shell
Norbert Heuer, Torsten Linß
We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of th…
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…
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…
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…
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…
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
Thomas Führer, Norbert Heuer, Francisco-Javier Sayas
We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-pose…
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 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…
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…
Finite element approximations of the nonhomogeneous fractional Dirichlet problem
Gabriel Acosta, Juan Pablo Borthagaray, Norbert Heuer
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and…
Combining the DPG method with finite elements
Thomas Führer, Norbert Heuer, Michael Karkulik +1
We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-adve…
On the DPG method for Signorini problems
Thomas Führer, Norbert Heuer, Ernst P. Stephan
We derive and analyze discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We…
Regularity of the Solution to 1-D Fractional Order Diffusion Equations
V. J. Ervin, N. Heuer, J. P. Roop
In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in . From an analysis of the underlying model problem,…
A time-stepping DPG scheme for the heat equation
Thomas Führer, Norbert Heuer, Jhuma Sen Gupta
We introduce and analyze a discontinuous Petrov-Galerkin method with optimal test functions for the heat equation. The scheme is based on the backward Euler time stepping and uses…
Robust coupling of DPG and BEM for a singularly perturbed transmission problem
Thomas Führer, Norbert Heuer
We consider a transmission problem consisting of a singularly perturbed reaction diffusion equation on a bounded domain and the Laplacian in the exterior, connected through standar…
A robust DPG method for singularly perturbed reaction-diffusion problems
Norbert Heuer, Michael Karkulik
We present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start wit…