Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations

Thomas Peter Fries, Hermann Georg Matthies

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Abstract

Meshfree stabilised methods are employed and compared for the solution of the incompressible Navier-Stokes equations in Eulerian formulation. These Petrov-Galerkin methods are standard tools in the FEM context, and can be used for meshfree methods as well. However, the choice of the stabilisation parameter has to be reconsidered. We find that reliable and successful approximation with standard formulas for the stabilisation parameter can only be expected for shape functions with small supports or dilatation parameters.

Original languageEnglish
Title of host publicationMeshfree Methods for Partial Differential Equations II
Pages39-54
Number of pages16
Volume43
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computational Science and Engineering
Volume43
ISSN (Print)14397358

Fingerprint

Petrov-Galerkin Method
Meshfree Method
Incompressible Navier-Stokes Equations
Galerkin methods
Navier Stokes equations
Stabilization
Stabilized Methods
Dilatation
Shape Function
Finite element method
Formulation
Approximation
Standards

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mathematics
  • Modelling and Simulation
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Fries, T. P., & Matthies, H. G. (2005). Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations. In Meshfree Methods for Partial Differential Equations II (Vol. 43, pp. 39-54). (Lecture Notes in Computational Science and Engineering; Vol. 43).

Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations. / Fries, Thomas Peter; Matthies, Hermann Georg.

Meshfree Methods for Partial Differential Equations II. Vol. 43 2005. p. 39-54 (Lecture Notes in Computational Science and Engineering; Vol. 43).

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Fries, TP & Matthies, HG 2005, Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations. in Meshfree Methods for Partial Differential Equations II. vol. 43, Lecture Notes in Computational Science and Engineering, vol. 43, pp. 39-54.
Fries TP, Matthies HG. Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations. In Meshfree Methods for Partial Differential Equations II. Vol. 43. 2005. p. 39-54. (Lecture Notes in Computational Science and Engineering).
Fries, Thomas Peter ; Matthies, Hermann Georg. / Meshfree Petrov-Galerkin methods for the incompressible Navier-Stokes equations. Meshfree Methods for Partial Differential Equations II. Vol. 43 2005. pp. 39-54 (Lecture Notes in Computational Science and Engineering).
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