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!!!!!!!!!!! !!!!!!!!!!! !!!!!!!!!!! Eidgenössische
!!!!!!!!!!! !!!!!!!!!!! !!!!!!!!!!! Technische Hochschule
!!!!!!!!!!! !!!!!!!!!!! !!!!!!!!!!! Zürich
Ecole polytechnique fédérale de Zurich
Politecnico federale di Zurigo
Swiss Federal Institute of Technology Zurich
hp FEM for incompressible fluid flow stable and stabilized
K. Gerdes and D. Schötzau
Research Report No. 97-18
December 1997
Seminar für Angewandte Mathematik
Eidgenössische Technische Hochschule
CH-8092 Zürich
Switzerland
hp FEM for incompressible fluid flow - stable and stabilized
K. Gerdes and D. Schötzau
Seminar für Angewandte Mathematik
Eidgenössische Technische Hochschule
CH-8092 Zürich
Switzerland
Research Report No. 97-18
December 1997
Abstract
The stable Galerkin formulation and a stabilized Galerkin Least Squares
formulation for the Stokes problem are analyzed in the context of the hpversion of the Finite Element Method (FEM). Theoretical results for both
formulations establish exponential rates of convergence and are confirmed by
intensive numerical convergence studies. In our numerical experiments we
demonstrate that these hp−FEM with geometric mesh refinement can resolve
corner singularities at an exponential rate.
Keywords: hp Finite Element Method (hp-FEM), Stokes problem, Galerkin formulation, Galerkin Least Squares formulation
Subject Classification: Primary: 65N30, 65N35, Secondary: 65N50
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Research Reports
No.
Authors
97-18 K. Gerdes, D. Schötzau
97-17
97-16
97-15
97-14
97-13
97-12
97-11
97-10
97-09
97-08
97-07
97-06
97-05
97-04
97-03
97-02
97-01
Title
hp FEM for incompressible fluid flow - stable
and stabilized
L. Demkowicz, K. Gerdes, HP90: A general & flexible Fortran 90 hp-FE
C. Schwab, A. Bajer,
code
T. Walsh
R. Jeltsch, P. Klingenstein Error Estimators for the Position of Discontinuities in Hyperbolic Conservation Laws with
Source Terms which are solved using Operator Splitting
C. Lage, C. Schwab
Wavelet Galerkin Algorithms for Boundary
Integral Equations
D. Schötzau, C. Schwab, Mixed hp - FEM on anisotropic meshes II:
R. Stenberg
Hanging nodes and tensor products of boundary layer meshes
J. Maurer
The Method of Transport for mixed hyperbolic - parabolic systems
M. Fey, R. Jeltsch,
The method of transport for nonlinear sysJ. Maurer, A.-T. Morel
tems of hyperbolic conservation laws in several space dimensions
K. Gerdes
A summary of infinite element formulations
for exterior Helmholtz problems
R. Jeltsch, R.A. Renaut, An Accuracy Barrier for Stable Three-TimeJ.H. Smit
Level Difference Schemes for Hyperbolic
Equations
K. Gerdes, A.M. Matache, Analysis of membrane locking in hp FEM for
C. Schwab
a cylindrical shell
T. Gutzmer
Error Estimates for Reconstruction using
Thin Plate Spline Interpolants
J.M. Melenk
Operator
Adapted
Spectral
Element
Methods. I. Harmonic and Generalized Harmonic Polynomials
C. Lage, C. Schwab
Two Notes on the Implementation of Wavelet
Galerkin Boundary Element Methods
J.M. Melenk, C. Schwab
An hp Finite Element Method for convectiondiffusion problems
J.M. Melenk, C. Schwab
hp FEM for Reaction-Diffusion Equations.
II. Regularity Theory
J.M. Melenk, C. Schwab
hp FEM for Reaction-Diffusion Equations.
I: Robust Exponentiel Convergence
D. Schötzau, C. Schwab
Mixed hp-FEM on anisotropic meshes
R. Sperb
Extension of two inequalities of Payne