An h-adaptive SUPG-FEM solution of the pure advection equation

Applied Numerical Mathematics

Volumn 26, Issue 1-2, 1998, Pages 193-202

  Usmani, Asif S ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; EQUATIONS OF MOTION; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING;

ADAPTIVE FINITE ELEMENT METHOD; PURE ADVECTION EQUATION; STREAMLINE UPWIND PETROV-GALERKIN (SUPG);

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031640206     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00087-1     Document Type: Article

References (14)

1. A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259.
2. J. Donea, A Taylor-Galerkin method for convective transport problems, Internat. J. Numer. Methods Engrg. 20 (1984) 101-119.
3. E. Hinton and J.S. Campbell, Local and global smoothing of discontinuous finite element functions using a least squares method, Internat. J. Numer. Methods Engrg. 8 (1974) 461-480.
4. H.C. Huang and A.S. Usmani, Finite Element Analysis for Heal Transfer - Theory and Software (Springer, London, 1994).
5. T.J.R. Hughes, The Finite Element Method - Linear Static and Dynamic Finite Element Analysis (Prentice-Hall, Englewood Cliffs, NJ. 1987).
6. T.J.R. Hughes, M. Mallet and A. Mizukami, A new finite element formulation for computational fluid dynamics: Ii. beyond supg., Comput. Methods Appl. Mech. Engrg. 54 (1986) 341-355.
7. R.W. Lewis, H.C. Huang, A.S. Usmani and J.T. Cross, Finite element analysis of heat transfer and flow problems using adaptive remeshing including application to solidification, Internat. J. Numer. Methods Engrg. 32 (1991) 767-781.
8. R.W. Lewis, A.S. Usmani and H.C. Huang, Casting modeling by finite elements - our experience, in: Proceedings of the 5th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, Davos, Switzerland, September 1990 (The Minerals, Metals and Materials Society, 1990) 3-14.
9. R. Lohner, K. Morgan and O.C. Zienkiewicz, Adaptive grid refinement for the compressible Euler equations, in: I. Babuška, ed., Accuracy Estimates and Adaptive Refinements in Finite Element Computations (Wiley, New York, 1986) 281.
10. A. Tessler, H.R. Riggs and S.C. Macy, A variational method for finite element stress recovery and error estimation, Comput. Methods Appl. Mech. Engrg. 111 (1994) 369-382.
11. O.C. Zienkiewicz, Y.C. Liu and G.C. Huang, Error estimates and convergence rates for various incompressible elements, Internat. J. Numer. Methods Engrg. 28 (1989) 2191-2202.
12. O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg. 24 (1987) 337-357.
13. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Part 2: Error estimates and adaptivity, Internat. J. Numer. Methods Engrg. 33 (1992) 1331-1382.
14. M. Zlamal, Supcrconvergencc and reduced integration in the finite element method, Math. Comp. 32 (1978) 663-685.