AN UPSTREAM PSEUDOSTRESS-VELOCITY MIXED FORMULATION FOR THE OSEEN EQUATIONS

Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation

In this paper, we develop and analyze mixed finite element methods for the Stokes and Navier-Stokes equations. Our mixed method is based on the pseudostress-pressure-velocity formulation. The pseudostress is approximated by the Raviart-Thomas, Brezzi-Douglas-Marini, or Brezzi-DouglasFortin-Marini elements, the pressure and the velocity by piecewise discontinuous polynomials of appropriate degre...

Guaranteed Velocity Error Control for the Pseudostress Approximation of the Stokes Equations

The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in H(div) and the velocity in L2. Any standard mixed finite element function space can be utilized for this mixed formulation, e.g., the Raviart-Thomas discretization which is r...

A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem

The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori...

A Multigrid Method for the Pseudostress Formulation of Stokes Problems

The purpose of this paper is to develop and analyze a multigrid solver for the finite element discretization of the pseudostress system associated with the differential operator A − γ graddiv over 2 × 2 matrix-valued functions. This system is derived from the pseudostressvelocity formulation [11] of two-dimensional Stokes problems through the penalty method or natural time discretization for th...

A preconditioner for the 3D Oseen equations