A Finite Element Variational Multiscale Method for the Navier-Stokes Equations

Multi-level hp-FEM and the Finite Cell Method for the Navier-Stokes equations using a Variational Multiscale Formulation

Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations

An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element metho...

Consistent Newton-Raphson vs. fixed-point for variational multiscale formulations for incompressible Navier-Stokes

The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompress-ible Navier–Stokes. The main contributions of this work include a consistent linearization of the Navier–Stokes equations, which provides an avenue for advanced algorithms that require origins in a consistent method. We...

Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

Convergence towards weak solutions of the Navier-Stokes for a finite element approximation with numerical subgrid scale modeling

Residual-based stabilized finite element techniques for the NavierStokes equations lead to numerical discretizations that provide convection stabilization as well as pressure stability without the need to satisfy an inf-sup condition. They can be motivated by using a variational multiscale framework, based on the decomposition of the fluid velocity into a resolvable finite element component plu...