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An h-p adaptive finite element method for the numerical simulation of compressible flow. (English) Zbl 0636.76064

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
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[1] Abramowitz, M.; Stegun, I., ()
[2] Babuška, I.; Rheinboldt, W.C., Reliable error estimation and mesh adaptation for the finite element method, () · Zbl 0451.65078
[3] Babuška, I.; Rheinboldt, W.C., Error estimates for adaptive finite element computations, SIAM J. numer. anal., 15, 4, (1978) · Zbl 0398.65069
[4] Bank, R.E.; Sherman, A.H., A refinement algorithm and dynamic data structure for finite element meshes, () · Zbl 0466.65058
[5] Bey, K.S.; Thornton, E.A.; Dechaumphai, P.; Romakrashnan, R., A new finite element approach of prediction of aerothermal loads, ()
[6] Carter, J.E., Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner, Nasa tr r-385, 21-29, (1972)
[7] P. Dechaumphai, Mach 3 flow over flat plate: A comparison of finite element results with Carter’s solution, Tech. Rept., Mechanical Engineering and Mechanics Department, Old Dominion University, Norfolk, VA.
[8] Demkowicz, L.; Devloo, Ph.; Oden, J.T., On an \(h- type\) mesh refinement strategy based on minimization of interpolation errors, Comput. meths. appl. mech. engrg., 35, 67-90, (1985) · Zbl 0556.73081
[9] Demkowicz, L.; Oden, J.T., An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables, Comput. meths. appl. mech. engrg., 55, 63-87, (1986) · Zbl 0602.76097
[10] Dendy, J.E., Two methods of Galerkin-type achieving optimum \(L2\) accuracy for first order hyperbolics, SIAM J. numer. anal., 11, 637-653, (1974) · Zbl 0293.65077
[11] Devloo, Ph.; Hayes, L.J., A fast vector algorithm for a matrix vector multiplication with the finite element method, ()
[12] Devloo, Ph.; Oden, J.T.; Strouboulis, T., Implementation of an adaptive refinement technique for the SUPG algorithm, Comput. meths. appl. mech. engrg, 61, 339-358, (1987) · Zbl 0596.73066
[13] Douglas, J.; Dupont, T.; Wheeler, M., A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems, Rairo, 47-59, (1974) · Zbl 0315.65063
[14] Eiseman, P., Adaptive grid generation, Comput. meths. appl. mech. engrg., 64, 321-376, (1987) · Zbl 0636.65126
[15] P.M. Gresho and R.L. Lee, The consistent Galerkin FEM for computing derived boundary quantities in thermal and/or fluid problems, preprint. · Zbl 0629.76095
[16] Guo; Babuška, I., The h-p version of the finite element method, Comput. mech., 1, 1, 21-42, (1986), Part 1 · Zbl 0634.73058
[17] Hughes, T.J.R.; Brooks, A., A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions application to the streamline-upwind procedure, (), 47-65
[18] Hughes, T.J.R.; Tezduyar, T.E., Finite element methods for first order hyperbolic systems with particular emphasis on the compressible Euler calculations, Comput. meths. appl. mech. engrs., 45, 217-284, (1984) · Zbl 0542.76093
[19] Hughes, T.J.R.; Franca, L.P.; Mallet, M., 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, Comput. meths. appl. mechs. engrg., 54, 223-234, (1986) · Zbl 0572.76068
[20] Hughes, T.J.R.; Franca, L.P.; Harari, I.; Mallet, M.; Shakib, F.; Spelce, T.E., Finite element method for high-speed flows: consistent calculation of boundary flux, ()
[21] Hughes, T.J.R.; Mallet, M., A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, Comput. meths. appl. mechs. engrg., 58, 329-336, (1986) · Zbl 0587.76120
[22] Jameson, A., Solution of the Euler equations for two-dimensional transonic flow by a multigrid method, Appl. math. comput., 13, 327-355, (1983) · Zbl 0545.76065
[23] Johnson, C.; Nävert, U.; Pitkäranta, J., Finite element methods for linear hyperbolic problems, Comput. meths. appl. mechs. engrg., 46, 285-312, (1984) · Zbl 0526.76087
[24] Lax, P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, () · Zbl 0108.28203
[25] Löhner, R., An adaptive finite element scheme for transient problems in CFD, Comput. meths. appl. mech. engrg., 61, 323-338, (1987) · Zbl 0611.73079
[26] Y. Maday and A. Patera, Spectral element methods for the incompressible Navier Stokes equations, in: A. K. Noor and J.T. Oden, eds., State-of-the-Art Surveys in Computational Mechanics (ASME, New York, to appear).
[27] Mallet, M., A finite element method of computational fluid dynamics, ()
[28] Oden, J.T.; Strouboulis, T.; Devloo, Ph.; Howe, M., Recent advances in error estimation and adaptive improvement of finite element calculations, (), 369-410
[29] Oden, J.T.; Demkowicz, L.; Strouboulis, T.; Devloo, Ph., Adaptive methods for problems in solid and fluid mechanics, ()
[30] Oden, J.T.; Demkowicz, L., Advances in adaptive improvements: A survey of adaptive finite element methods in computational mechanics, () · Zbl 0602.76097
[31] Patera, A., A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. comput. phys., 54, 486, (1984)
[32] Szabó, B.A., Estimation and control of error based on \(p\) convergence, ()
[33] Wahlbin, L.B., A dissipative Galerkin method for the numerical solution of first order hyperbolic equations, (), 147-169
[34] Warming, R.F.; Beam, R.M.; Hyett, B.J., Diagonalization and simultaneous symmetrization of the gas dynamics nmatric, Math, comput., 29, 132, 1037-1045, (1975) · Zbl 0313.65084
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