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 …

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 …

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 …

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 …

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 …

We consider a space-time variational formulation of parabolic initial-boundary value
problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation …

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 …

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 …

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 …

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 …