Space–time least-squares finite elements for parabolic equations
T Führer, M Karkulik - Computers & Mathematics with Applications, 2021 - Elsevier
We present a space–time least-squares finite element method for the heat equation. It is
based on residual minimization in L 2 norms in space–time of an equivalent first order …
based on residual minimization in L 2 norms in space–time of an equivalent first order …
Design and performance of a space–time virtual element method for the heat equation on prismatic meshes
We present a space–time virtual element method for the discretization of the heat equation,
which is defined on general prismatic meshes and variable degrees of accuracy. Strategies …
which is defined on general prismatic meshes and variable degrees of accuracy. Strategies …
Least squares solvers for ill-posed PDEs that are conditionally stable
W Dahmen, H Monsuur… - … Modelling and Numerical …, 2023 - esaim-m2an.org
This paper is concerned with the design and analysis of least squares solvers for ill-posed
PDEs that are conditionally stable. The norms and the regularization term used in the least …
PDEs that are conditionally stable. The norms and the regularization term used in the least …
Space-time virtual elements for the heat equation
We propose and analyze a space-time virtual element method for the discretization of the
heat equation in a space-time cylinder, based on a standard Petrov–Galerkin formulation …
heat equation in a space-time cylinder, based on a standard Petrov–Galerkin formulation …
[HTML][HTML] Review and computational comparison of adaptive least-squares finite element schemes
P Bringmann - Computers & Mathematics with Applications, 2024 - Elsevier
The convergence analysis for least-squares finite element methods led to various adaptive
mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori …
mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori …
Applications of a space-time FOSLS formulation for parabolic PDEs
G Gantner, R Stevenson - IMA Journal of Numerical Analysis, 2024 - academic.oup.com
In this work, we show that the space-time first-order system least-squares formulation
(Führer, T. & Karkulik, M.(2021) Space–time least-squares finite elements for parabolic …
(Führer, T. & Karkulik, M.(2021) Space–time least-squares finite elements for parabolic …
[HTML][HTML] Improved rates for a space–time FOSLS of parabolic PDEs
G Gantner, R Stevenson - Numerische Mathematik, 2024 - Springer
We consider the first-order system space–time formulation of the heat equation introduced
by Bochev and Gunzburger (in: Bochev and Gunzburger (eds) Applied mathematical …
by Bochev and Gunzburger (in: Bochev and Gunzburger (eds) Applied mathematical …
Least-squares finite elements for distributed optimal control problems
T Führer, M Karkulik - Numerische Mathematik, 2023 - Springer
We provide a framework for the numerical approximation of distributed optimal control
problems, based on least-squares finite element methods. Our proposed method …
problems, based on least-squares finite element methods. Our proposed method …
Well-posedness of first-order acoustic wave equations and space-time finite element approximation
T Führer, R González, M Karkulik - arXiv preprint arXiv:2311.10536, 2023 - arxiv.org
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 L^ 2 …
operator of this system is an isomorphsim from an appropriately defined graph space to L^ 2 …
Minimal residual methods in negative or fractional Sobolev norms
H Monsuur, R Stevenson, J Storn - Mathematics of Computation, 2024 - ams.org
For numerical approximation the reformulation of a PDE as a residual minimisation problem
has the advantages that the resulting linear system is symmetric positive definite, and that …
has the advantages that the resulting linear system is symmetric positive definite, and that …