The finite element method is the most popular general purpose technique for computing
accurate solutions to partial differential equations (PDEs). Since PDEs form the basis for …

In this paper we introduce and analyze a virtual element method (VEM) for a mixed
variational formulation of the Stokes problem in which the pseudostress and the velocity are …

We investigate a family of isotropic volumetric-isochoric decoupled strain energies F ↦ W_
eH (F):= W _ eH (U):=\left {μ ke^ k ‖ dev _n U ‖^ 2+ κ 2 ke^ k tr (\log U)^ 2 & if\det F> …

This paper develops and analyzes two least-squares methods for the numerical solution of
linear, stationary incompressible Newtonian fluid flow in two and three dimensions. Both …

We consider a non-standard mixed approach for the Stokes problem in which the velocity,
the pressure, and the pseudostress are the main unknowns. Alternatively, the pressure can …

In this article, we develop and analyze a mixed finite element method for the Stokes
equations. Our mixed method is based on the pseudostress‐velocity formulation. The …

We consider divergence-based high order discretizations of an L 2-based first order system
least squares formulation of a second order elliptic equation with Robin boundary …

In this paper we introduce and analyze a new mixed finite element method for the two-
dimensional Brinkman model of porous media flow with mixed boundary conditions. We use …

A new mixed variational formulation for the Navier--Stokes equations with constant density
and variable viscosity depending nonlinearly on the gradient of velocity, is proposed and …

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 …