Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
R Stevenson, J Westerdiep - IMA Journal of Numerical Analysis, 2021 - academic.oup.com
We analyze Galerkin discretizations of a new well-posed mixed space–time variational
formulation of parabolic partial differential equations. For suitable pairs of finite element trial …
formulation of parabolic partial differential equations. For suitable pairs of finite element trial …
Further results on a space-time FOSLS formulation of parabolic PDEs
G Gantner, R Stevenson - ESAIM: Mathematical Modelling and …, 2021 - esaim-m2an.org
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:
1911.01942] by Führer and Karkulik, well-posedness of a space-time First-Order System …
1911.01942] by Führer and Karkulik, well-posedness of a space-time First-Order System …
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 hp-finite elements for heat evolution in laser powder bed fusion additive manufacturing
The direct numerical simulation of metal additive manufacturing processes such as laser
powder bed fusion is challenging due to the vast differences in spatial and temporal scales …
powder bed fusion is challenging due to the vast differences in spatial and temporal scales …
Efficient direct space-time finite element solvers for parabolic initial-boundary value problems in anisotropic Sobolev spaces
U Langer, M Zank - SIAM Journal on Scientific Computing, 2021 - SIAM
We consider a space-time variational formulation of parabolic initial-boundary value
problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation …
problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation …
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 …
Adaptive least-squares space-time finite element methods
C Köthe, R Löscher, O Steinbach - arXiv preprint arXiv:2309.14300, 2023 - arxiv.org
We consider the numerical solution of an abstract operator equation $ Bu= f $ by using a
least-squares approach. We assume that $ B: X\to Y^* $ is an isomorphism, and that $ A …
least-squares approach. We assume that $ B: X\to Y^* $ is an isomorphism, and that $ A …
[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 …