Publication

Pressure projection Stabilizations for Galerkin approximations of Stokes' and Darcy's problem

Erik Burman
2008
Journal Articles

Abstract

In this study, we consider some recent stabilization techniques for the Stokes' problem and show that they are instances of the framework proposed by Brezzi and Fortin in "A minimal stabilisation procedure for mixed finite element methods" (Numer Math 89, (2001) 457). We also propose an analysis for Taylor-Hood elements with discontinuous pressures stabilized using penalization of the interelement pressure jumps. (c) 2007 Wiley Periodicals, Inc.

Official source

https://infoscience.epfl.ch/entities/publication/3e69e12c-8e4e-4973-a862-eaf09ac7cdd4

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Erik Burman
2008
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3e69e12c-8e4e-4973-a862-eaf09ac7cdd4

About this result

Related concepts (6)

Galerkin method

In mathematics, in the area of numerical analysis, Galerkin methods are named after the Soviet mathematician Boris Galerkin. They convert a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Meshfree methods

In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.

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