Abstract
We give an overview of some recent theoretical and computational results for streamline diffusion finite element methods applied to the incompressible Navier-Stokes equations with small viscosity and to some nonlinear hyperbolic conservation laws modelling compressible flow.
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References
R.J. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. 82(1983) pp. 27–70.
K. Eriksson and C. Johnson, An adaptive finite element method for linear elliptic problems, Technical report, Chalmers University of Technology, to appear in Math. Comp.
P. Hansbo, Finite element procedures for conduction and convection problems, Publication 86:7, Dept. of Structural Mechanics, Chalmers Univ. of Technology.
A. Harten, On the symmetric form of systems of conservation laws with entropy. Journal of Computational Physics 49 (1983) pp. 151–164.
T.J.R. Hughes and A. Brooks, A multidimensional upwind scheme with no crosswing diffusion, in AMD vol 34, Finite Element Methods for Convection Dominated Flows (T.J. Hughes ed.), ASME, New York 1979.
T.J.R. Hughes, E.t. Tezduyar and A. Brooks, Streamline Upwind Formulation for Advection-Diffusion, Navier-Stokes and First Order Hyperbolic Equations, Fourth Internat. Conf. on Finite Element Methods in Fluids, Tokyo, July 1982.
T.J.R. Hughes and T.E. Tezduyar, Finite Element Methods for First-Order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations, Computer Methods in Applied Mechanics and Engineering, Vol. 45(1984), pp. 217–284.
T.J.R. Hughes, M. Mallet and L.P. Franca, Entropy-stable finite element methods for compressible fluids: Application to high mach number flows with shocks, to appear in Finite Element Methods for Nonlinear Problems (eds. P. Bergan et al.), Springer-Verlag.
T.J.R. Hughes, L.P. Franca and M. Mallet, A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes Equations and the second law of thermodynamics, to appear in Computer Methods in Applied Mechanics and Engineering.
T.J.R. Hughes, M. Mallet and A. Mizukami, A new element formulation for computational fluid dynamics: II. Beyond SUPG, to appear in Computer Methods in Applied Mechanics and Engineering.
T.J.R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics:: III. The generalized streamline operator for multidimensional advective-diffusive systems, to appear in Computer Methods in Applied Mechanics and Engineering.
T.J.R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics: IV. A discontinuity capturing operator for multidimensional advective-diffusive systems, to appear in Computer Methods in Applied Mechanics and Engineering.
C. Johnson and U. Nävert, An analysis of some finite element methods for advection-diffusion, in Analytical and Numerical Approaches to Asymptotic Problems in Analysis (eds. Axelsson et al), North-Holland, 1981.
C. Johnson, U. Nävert and J. Pitkäranta, Finite element methods for linear hyperbolic problems, Computer Methods in Appl. Mech. Eng. 45(1985), pp. 285–312.
C. Johnson and J. Saranen, Streamline diffusion methods for the incompressible Euler and Navier-Stokes equation, Math. Comp. 47(1986), pp.1–18.
C. Johnson, Streamline diffusion methods for problems in fluid mechanics, in Finite Elements in Fluids, ed. Gallagher et al, Wiley 1985.
C. Johnson and A. Szepessy, Convergence of a finite element method for a nonlinear hyperbolic conservation law, Technical report, Mathematics Dept. Chalmers Univ. of Technology, Göteborg, to appear in Math. Comp.
C. Johnson and A. Szepessy, On the convergence of streamline diffusion finite element methods for hyperbolic conservation laws, Proc. ASME conference, Anaheim dec. 1986.
U. Nävert, A Finite Element Method for Convection-Diffusion Problems, Thesis, Chalmers University of Technology, Göteborg 1982.
A. Szepessy, A streamline diffusion finite element method for the incompressible Navier-Stokes equations in three dimensions, to appear.
E. Tadmor, Skew-selfadjoint forms for systems of conservation laws, Journal of Mathematical Analysis and Applications, Vol. 103(1984), pp. 428–442.
L. Tartar, Compensated compactness and applications to partial differential equations, in Research notes in Mathematics, Nonlinear analysis and mechanics: Heriot-Watts Symposium, Vol. 4. ed. R.J. Knops, Pitman Press (1979).
K. Eriksson and C. Johnson, An adaptive finite element method for linear advection problems, to appear.
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© 1988 Springer-Verlag New York Inc.
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Johnson, C. (1988). Streamline Diffusion Finite Element Methods for Incompressible and Compressible Fluid Flow. In: Engquist, B., Majda, A., Luskin, M. (eds) Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3882-9_6
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DOI: https://doi.org/10.1007/978-1-4612-3882-9_6
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