Quantitative error control for finite element methods for one-dimensional compressible flow

SIAM Journal on Numerical Analysis

Volumn 35, Issue 5, 1998, Pages 2014-2034

  Sandboge, Robert ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

A posteriori error estimates; Compressible flow; Error control; Euler equations; Finite elements; Strong stability

Indexed keywords

EID: 0006445753     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997321625     Document Type: Article

References (17)

1. F. BOURDEL, J.-P. CROISILLE, P. DELORME, AND P.-A. MAZET, On the approximation of K-diagonalizable hyperbolic systems by finite elements. Applications to the Euler equations and to gaseous mixtures, Rech. Aérospat., 5 (1989), pp. 15-34.
2. E. BURMAN AND R. SANDBOGE, Finite element methods for compressible flow, to appear.
3. F. CHALOT, T. J. R. HUGHES, AND F. SHAKIB, Symmetrization of conservation laws with entropy for high-temperature hypersonic computations, Comput. Systems Engrg., 1 (1990), pp. 495-521.
4. K. ERIKSSON, D. ESTEP, P. HANSBO, AND C. JOHNSON, Computational Differential Equations, Cambridge University Press, London, 1996.
5. P. HANSBO, Explicit streamline diffusion finite element methods for the compressible Euler equations in conservation variables, J. Comput. Phys., 109 (1993), pp. 274- 288.
6. P. HANSBO, Space-time oriented streamline diffusion methods for nonlinear conservation laws in one dimension, Comm. Numer. Methods Engrg., 10 (1994), pp. 203-215.
7. P. HANSBO AND C. JOHNSON, Adaptive streamline diffusion finite element methods for compressible flow using conservation variables, Comput. Methods Appl. Mech. Engrg., 87 (1991), pp. 267-280.
8. P. HANSBO AND C. JOHNSON, Space-Time Oriented Streamline Diffusion Finite Element Methods for Compressible Flow on the CM-2, Internal report, Department of Mathematics, Chalmers University of Technology, Göteborg, Sweden, 1993.
9. C. JOHNSON AND A. SZEPESSY, Adaptive finite element methods for conservation laws based on a posteriori error estimates, Comm. Pure Appl. Math., 48 (1995), pp. 199- 134.
10. C. JOHNSON, The characteristic streamline diffusion finite element method, Math. Appl. Comput., 10 (1991), pp. 229-242.
11. C. JOHNSON, A new approach to algorithms for convection problems which are based on exact transport + projection, Comp. Methods Appl. Mech. Engrg., 100 (1992), pp. 45-62.
12. C. JOHNSON, A. SZEPESSY, AND P. HANSBO, On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws, Math. Comp., 54 (1990), pp. 107-129.
13. M. G. LARSON, Adaptive Finite Element Methods for the Euler Equations in One Dimension, Preprint 1995:01, Department of Mathematics, Chalmers University of Technology, Göteborg, Sweden, 1995.
14. F. SHAKIB, T. J. R. HUGHES, AND Z. JOHAN, A new finite element method for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 89 (1991), pp. 141-219.
15. G. A. SOD, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys., 27 (1978), pp. 1-31.
16. J. R. STEWART AND T. J. R. HUGHES, Explicit residual-based a posteriori error estimation for the finite element discretizations of the Helmholtz equation: Computation of the constant and new measure of error estimator quality, Comp. Methods Appl. Mech. Engrg., 131 (1996), pp. 335-363.
17. A. SZEPESSY, Convergence of the Streamline Diffusion Finite Element Method for Conservation Laws, Thesis, Department of Mathematics, Chalmers University of Technology, Göteborg, Sweden, 1989.