Browsing by Author "Führer, Thomas"
Now showing 1 - 20 of 42
Results Per Page
Sort Options
- ItemA Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates(2023) Führer, Thomas; Heuer, Norbert; Niemi, Antti H.We present a discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.
- ItemA DPG method for linear quadratic optimal control problems(Elsevier Ltd, 2024) Führer, Thomas; Fuica Villagra, FranciscoThe 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 solution of the nonlinear discrete problem and characterize it through first-order optimality conditions. Furthermore, we systematically develop a priori as well as a posteriori error estimates. Our proposed method can be applied to a wide range of constrained optimal control problems subject to, e.g., scalar second-order PDEs and the Stokes equations. Numerical experiments that illustrate our theoretical findings are presented.
- ItemA linear Uzawa-type FEM-BEM solver for nonlinear transmission problems(2018) Führer, Thomas; Praetorius, Dirk
- ItemA locking-free DPG scheme for Timoshenko beams(2020) Führer, Thomas; García Vera, Carlos Mauricio; Heuer, Norbert
- ItemA robust DPG method for large domains(2021) Führer, Thomas; Heuer, NorbertWe observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincare-type inequality. We show how robustness can be re-established by using appropriately scaled test norms. As model cases we study the Poisson problem and the Kirchhoff-Love plate bending model, and also include fully discrete variants where optimal test functions are approximated. Numerical experiments for both model problems, including an-isotropic domains and mixed boundary conditions, confirm our findings.
- ItemA short note on plain convergence of adaptive least-squares finite element methods(2020) Führer, Thomas; Praetorius, D
- ItemA Time-Stepping DPG Scheme for the Heat Equation(2017) Führer, Thomas; Heuer, Norbert; Gupta J.
- ItemA wirebasket preconditioner for the mortar boundary element method(2018) Führer, Thomas; Heuer, Norbert
- ItemAdaptive BEM with inexact PCG solver yields almost optimal computational costs(2019) Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan
- ItemAdaptive Boundary Element Methods A Posteriori Error Estimators, Adaptivity, Convergence, and Implementation(2015) Feischl, M.; Führer, Thomas; Heuer, Norbert; Karkulik, Michael; Praetorius, D.
- ItemAdaptive boundary element methods for optimal convergence of point errors(2016) Feischl, M.; Gantner, G.; Haberl, A.; Praetorius, D.; Führer, Thomas
- ItemAdaptive Uzawa algorithm for the Stokes equation(2019) Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk
- ItemAN ULTRAWEAK FORMULATION OF THE KIRCHHOFF-LOVE PLATE BENDING MODEL AND DPG APPROXIMATION(2019) Führer, Thomas; Heuer, Norbert; Niemi, Antti H.
- ItemAn ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation(2020) Führer, Thomas; Heuer, Norbert; Sayas, F. J.
- ItemAnalysis of Backward Euler Primal DPG Methods(2021) Führer, Thomas; Heuer, Norbert; Karkulik, MichaelWe analyze backward Euler time stepping schemes for a primal DPG formulation of a class of parabolic problems. Optimal error estimates are shown in a natural norm and in the L-2 norm of the field variable. For the heat equation the solution of our primal DPG formulation equals the solution of a standard Galerkin scheme and, thus, optimal error bounds are found in the literature. In the presence of advection and reaction terms, however, the latter identity is not valid anymore and the analysis of optimal error bounds requires to resort to elliptic projection operators. It is essential that these operators be projections with respect to the spatial part of the PDE, as in standard Galerkin schemes, and not with respect to the full PDE at a time step, as done previously.
- ItemDPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation(2017) Ervin, V.; Führer, Thomas; Heuer, Norbert; Karkulik, Michael
- ItemDPG Methods for a Fourth-Order div Problem(2022) Führer, Thomas; Herrera Ortiz, Pablo Cesar; Heuer, NorbertWe 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 second-order systems. In both cases, we prove well-posedness of the formulation and quasi-optimal convergence of the approximation. Our analysis includes the fully-discrete schemes with approximated test functions, for general dimension and polynomial degree in the first-order case, and for two dimensions and lowest-order approximation in the second-order case. Numerical results illustrate the performance for quasi-uniform and adaptively refined meshes.
- ItemFirst-order least-squares method for the obstacle problem(2020) Führer, Thomas
- ItemFirst-order system least-squares finite element method for singularly perturbed Darcy equations(2023) Führer, Thomas; Videman, JuhaWe define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-processing. It is shown that the least-squares functional is uniformly equivalent, i.e., independent of the singular perturbation parameter, to a parameter dependent norm. This norm equivalence implies that the least-squares functional evaluated in the discrete solution provides an efficient and reliable a posteriori error estimator. Numerical experiments are presented.
- ItemFully discrete DPG methods for the Kirchhoff-Love plate bending model(2019) Führer, Thomas; Heuer, Norbert
- «
- 1 (current)
- 2
- 3
- »