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 …

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 …

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 …

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 …

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 …

We provide a framework for the numerical approximation of distributed optimal control
problems, based on least-squares finite element methods. Our proposed method …

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 …

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 …