We investigate new PDE discretization approaches for solving variational formulations with
different types of trial and test spaces. The general mixed formulation we consider assumes …

The main goal of this contribution is the improvement of the approximation quality of least-
squares mixed finite elements for static and dynamic problems in quasi-incompressible …

We present a new least-squares finite element method for the steady Oldroyd type
viscoelastic fluids. The overall iterative procedure combines a nonlinear nested iteration …

We present a first-order system least-squares (FOSLS) method to approximate the solution
to the equations of geometrically nonlinear elasticity in two dimensions. With assumptions of …

In this paper, we present an approximation of elliptic problems with multiscale and high-
contrast diffusion coefficients. A mixed formulation is considered such that both pressure and …

A meshfree method based on the first-order least-squares formulation for linear elasticity is
presented. In the authors' previous work, the least-squares meshfree method has been …

In this contribution, we propose mixed least‐squares finite element formulations for
elastoplastic material behavior. The resulting two‐field formulations depending on …

First-order system least squares (FOSLS) was developed in [SIAM J. Numer. Anal., 34
(1997), pp. 1727--1741; SIAM J. Numer. Anal., 35 (1998), pp. 320--335] for Stokes and …

Different numerical methods have been proposed for the solution of partial differential
equations (PDE). Most of them are based on a variational principle which recasts the PDE …

The performance of least-squares finite element formulations for geometrically linear and
nonlinear problems is investigated in this work. We consider different elastic material …