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


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


Zbl 0455.76081
Full Text: DOI


[1] Brenner, P.; Thomée, V., Estimates near discontinuities for some difference schemes, Math. Scand., 27, 5-23 (1970) · Zbl 0208.16201
[2] Brooks, A., A Petrov-Galerkin finite element formulation for convective dominated flows, (Thesis (1981), CALTEC)
[3] Ciarlet, P. G., The finite Element Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam · Zbl 0445.73043
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.