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 …

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 …

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a
wide range of plasma physics systems, including the evolution of complex plasma dynamics …

The first-order div least squares finite element methods (LSFEMs) allow for an immediate a
posteriori error control by the computable residual of the least squares functional. This paper …

This paper studies finite element discretizations for three types of time-dependent PDEs,
namely heat equation, scalar conservation law and wave equation, which we reformulate as …

The first-order div least squares finite element methods provide inherent a posteriori error
estimator by the elementwise evaluation of the functional. In this paper we prove Q-linear …

This paper introduces the first adaptive least-squares finite element method (LS-FEM) for the
Stokes equations with optimal convergence rates based on the newest vertex bisection with …

We perform a followup computational study of the recently proposed space–time first order
system least squares (FOSLS) method subject to constraints referred to as CFOSLS where …

This paper investigates multilevel initialization strategies for training very deep neural
networks with a layer-parallel multigrid solver. The scheme is based on the continuous …

This paper studies adaptive first-order system least-squares finite element methods
(LSFEMs) for second-order elliptic partial differential equations in nondivergence form …