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Finite element methods for linear hyperbolic problems. (English) Zbl 0526.76087


MSC:

76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0455.76081
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References:

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[2] Brooks, A., A Petrov-Galerkin finite element formulation for convective dominated flows, (Thesis (1981), CALTEC)
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[4] Friedrichs, K. O., Symmetric positive differential equations, ((1958), CPAM), 333-418 · Zbl 0083.31802
[5] Hughes, T. J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, (Hughes, T. J.R., Finite Element Methods for Convection Dominated Flows, AMD, Vol. 34 (1979), ASME: ASME New York) · Zbl 0423.76067
[7] Hughes, T. J.R.; Tezduyar, T. E.; Brooks, A., Streamline upwind formulation for advection-diffusion, Navier-Stokes and first order hyperbolic equations, (Fourth Internat. Conf. on Finite Element Methods in Fluids. Fourth Internat. Conf. on Finite Element Methods in Fluids, Tokyo (1982)) · Zbl 0506.76026
[8] Jamet, P., Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain, SIAM J. Numer. Anal., 15, 912-928 (1978) · Zbl 0434.65091
[9] Johnson, C.; Nävert, U., An analysis of some finite element methods for advection-diffusion problems, (Axelsson, O.; Frank, L. S.; van der Sluis, A., Analytical and Numerical Approaches to Asymptotic Problems in Analysis (1981), North-Holland: North-Holland Amsterdam) · Zbl 0455.76081
[10] Johnson, C., Finite element methods for convection-diffusion problems, (Glowinski, R.; Lions, J. L., Computing Methods in Engineering and Applied Sciences V (1982), North-Holland: North-Holland Amsterdam) · Zbl 0505.76099
[11] Johnson, C.; Pitkäranta, J., Convergence of a fully discrete scheme for two-dimensional neutron transport, SIAM J. Numer. Anal., 20, 951-966 (1983) · Zbl 0538.65097
[12] Johnson, C.; Pitkäranta, J., An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, (Tech. Rept. (1984), Technical University of Helsinki) · Zbl 0618.65105
[14] Lesaint, P.; Raviart, P. A., On a finite element method for solving the neutron transport equation, (de Boor, C., Mathematical Aspects of Finite Elements in Partial Differential Equations (1974), Academic Press: Academic Press New York) · Zbl 0417.65056
[15] Lesaint, P., Sur la resolution des systemes hyperboliques du premier ordre par de methodes d’elements finis, These, Université Paris VI (1975)
[16] Nitsche, J.; Schatz, A., Interior estimates for Ritz-Galerkin methods, Math. Comput., 28, 937-958 (1974) · Zbl 0298.65071
[17] Nävert, U., A finite element method for convection-diffusion problems, (Thesis (1982), Chalmers Univ. of Technology: Chalmers Univ. of Technology Göteborg)
[18] Raithby, G. D., Skew upstream differencing schemes for problems involving fluid flow, Comput. Meths. Appl. Mech. Engrg., 9, 153-164 (1976) · Zbl 0347.76066
[19] Thomée, V., Some interior estimates for semidiscrete Galerkin approximations for parabolic equations, Math. Comput., 33, 37-62 (1979) · Zbl 0419.65073
[20] Amer. Math. Soc. Transl. Ser., 2 20, 239-364 (1962) · Zbl 0122.32402
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