Conservation Properties for the Galerkin and Stabilised Forms of the Advection-Diffusion and Incompressible Navier-Stokes Equations

Abstract

A common criticism of continuous Galerkin finite element methods is their perceived lack of conservation. This may in fact be true for incompressible flows when advective, rather than conservation, weak forms are employed. However, advective forms are often preferred on grounds of accuracy despite violation of conservation. It is shown here that this deficiency can be easily remedied, and conservative procedures for advective forms can be developed from multiscale concepts. As a result, conservative stabilised finite element procedures are presented for he advention-diffusion and imcompressible Navier-Stokes equations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2005
Accession Number
ADA438123

Entities

People

  • Garth N. Wells
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Advection
  • Boundaries
  • Boundary Value Problems
  • Civil Engineering
  • Continuity
  • Diffusion
  • Engineering
  • Equations
  • Finite Element Analysis
  • Flow
  • Flow Fields
  • Galerkin Method
  • Incompressible Flow
  • Navier Stokes Equations
  • Standards
  • Stratified Fluids
  • Time Domain

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design