Fitted finite element discretization of two-phase Stokes flow

A Stable Parametric Finite Element Discretization of Two-Phase Navier-Stokes Flow

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier–Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element appr...

Two-Level Finite Element Discretization of Viscoelastic Fluid Flow

Finite Element Discretization of the Stokes and Navier-Stokes Equations with Boundary Conditions on the Pressure

We consider the Stokes and Navier–Stokes equations with boundary conditions of Dirichlet type on the velocity on one part of the boundary and involving the pressure on the rest of the boundary. We write the variational formulations of such problems. Next we propose a finite element discretization of them and perform the a priori and a posteriori analysis of the discrete problem. Some numerical ...

Accurate multiscale finite element methods for two-phase flow simulations

In this paper we propose a modified multiscale finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the global fine-scale solution at initial time to determine the boundary conditions of the basis functions. This method provides a significant improvement in two-phase flow simulations in porous media where the long-range effect...

Unified Finite Element Discretizations of Coupled Darcy-stokes Flow

In this paper we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived form Darcy’s law in the rest of the domain, and where the solutions in the two domain are coupled by proper interface conditions. All the methods proposed here utilizes the same finite element space...