Revisiting stabilized finite element methods for the advective–diffusive equation

Parallel Adaptive Simulation of Coupled Incompressible Viscous Flow and Advective-Diffusive Transport Using Stabilized FEM Formulation

In this work we study coupled incompressible viscous flow and advective-diffusive transport of a scalar. Both the Navier-Stokes and transport equations are solved using an Eulerian approach. The SUPG/PSPG stabilized finite element formulation is applied for the governing equations. The implementation is held using the libMEsh finite element library which provides support for parallel adaptive m...

Unusual Stabilized Finite Element Methods for Second Order Linear Differential Equations

Unusual stabilized nite element methods are introduced here for linear second order equations. The method consists in subtracting to the standard Galerkin method a mesh dependent term composed by the adjoint operator applied to the test function multiplied by the residual of the Euler-Lagrange equation. The method is numerically tested for advective dominated and zero order dominated regimes, w...

A New Submesh Strategy in the Two-level Finite Element Method for the Advective-diffusive Equation

On an Improved Unusual Stabilized Finite Element Method for the Advective-Reactive-Di usive Equation

An improved unusual nite element method is studied herein for a second-order linear scalar diierential equation including a zero order term. The method consists in subtracting from the standard Galerkin method a mesh dependent term suggested by static condensation of the bubbles. Based on this idea, a new stabilized parameter is constructed, which improves accuracy of the solution. Several nume...

Multiscale and Stabilized Methods

This article presents an introduction to multiscale and stabilized methods, which represent unified approaches to modeling and numerical solution of fluid dynamic phenomena. Finite element applications are emphasized but the ideas are general and apply to other numerical methods as well. (They have been used in the development of finite difference, finite volume, and spectral methods, in additi...