Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems

Gert Lube

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 85-104
  • ISSN: 0137-6934

Abstract

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In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.

How to cite

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Lube, Gert. "Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems." Banach Center Publications 29.1 (1994): 85-104. <http://eudml.org/doc/262793>.

@article{Lube1994,
abstract = {In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.},
author = {Lube, Gert},
journal = {Banach Center Publications},
keywords = {diffusion-convection-reaction model; streamline upwind methods; elliptic boundary value problems; velocity/pressure interpolation functions; convergence; non-uniform meshes},
language = {eng},
number = {1},
pages = {85-104},
title = {Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems},
url = {http://eudml.org/doc/262793},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Lube, Gert
TI - Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 85
EP - 104
AB - In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.
LA - eng
KW - diffusion-convection-reaction model; streamline upwind methods; elliptic boundary value problems; velocity/pressure interpolation functions; convergence; non-uniform meshes
UR - http://eudml.org/doc/262793
ER -

References

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  15. [Tea] T. E. Tezduyar, R. Shih, S. Mittal and S. E. Ray, Incompressible flow computations with stabilized bilinear and linear equal-order interpolation velocity-pressure elements, preprint UMSI 90/165, Univ. of Minnesota, 1990. 
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