An adaptive stabilized finite element method for the Darcy’s equations with pressure dependent viscosities

An Absolutely Stable Pressure-Poisson Stabilized Finite Element Method for the Stokes Equations

The pressure-Poisson stabilized Galerkin method for the Stokes equation requires the choice of a positive parameter. Existing theoretical predictions for the range of parameter values that yield stable discretizations seem to be very pessimistic when compared to the computational evidence. Motivated by this wide gap, we first examine a continuous prototype for this class of schemes. We show tha...

A stabilized finite element method for the incompressible magnetohydrodynamic equations

We propose and analyze a stabilized nite element method for the incompressible magnetohydrodynamic equations. The numerical results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint. We explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation as soon as the hy...

An Adaptive Finite Element Method for the Incompressible Navier{stokes Equations on Time-dependent Domains

A fully discrete stabilized finite element method for the time-dependent Navier-Stokes equations

In this article, we consider a fully discrete stabilized finite element method based on two local Gauss integrations for the two-dimensional time-dependent Navier–Stokes equations. It focuses on the lowest equal-order velocity–pressure pairs. Unlike the other stabilized method, the present approach does not require specification of a stabilization parameter or calculation of higher-order deriva...

An Iterative Substructuring Method for the Discretized Stokes Equations by a Stabilized Finite Element Method

Abstract. A simple algorithm of iterative substructuring method as the same way of elasticity problem is proposed for a discretized Stokes equation by P1/P1 element and penalty stabilization technique. Owing to the stability term, solvabilities of local Dirichlet problem, of local Neumann problem for preconditioner, and of the coarse space problem are ensured. Conjugate gradient method with pre...