×

zbMATH — the first resource for mathematics

Discontinuous Galerkin finite element methods for second order hyperbolic problems. (English) Zbl 0787.65070
A finite element method for linear second order hyperbolic equations based on a space-time finite element discretization is considered. The basis functions are continuous in space and discontinuous in time. A priori and a posteriori error bounds are derived.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Eriksson, K.; Johnson, C., Adaptive finite element methods for linear parabolic problems I, SIAM J. numer. anal., 28, 43-77, (1991) · Zbl 0732.65093
[2] Eriksson, K., Adaptive finite element methods for linear parabolic problems II, optimal error estimates in L∞(L2) and L∞(L∞), (1992), Mathematics Department, Chalmers University of Technology, Preprint 1992-09
[3] Math. Comp., in press. · Zbl 0795.65074
[4] Hansbo, P.; Szepessy, A., A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 84, 175-192, (1990) · Zbl 0716.76048
[5] Hulbert, G.; Hughes, T.J.R., Space-time finite element methods for second-order hyperbolic equations, Comput. methods appl. mech. engrg., 84, 327-348, (1990) · Zbl 0754.73085
[6] Hughes, T.J.R.; Hulbert, G., Space-time finite element methods for elastodynamics: formulations and error estimates, Comput. methods appl. mech. engrg., 66, 339-363, (1988) · Zbl 0616.73063
[7] Hulbert, G., Space-time finite element methods for second order hyperbolic problems, ()
[8] C. Johnson, Adaptive finite element methods for diffusion and convection problems, Comput. Methods Appl. Mech. Engrg. 82 (90) 301-322. · Zbl 0717.76078
[9] Johnson, C., A new approach to algorithms for convection problems which are based on exact transport + projection, Comput. methods appl. mech. engrg., 100, 45-62, (1992) · Zbl 0825.76413
[10] Johnson, C.; Nävert, U.; Pitkäranta, J., Finite element methods for linear hyperbolic problems, Comput. methods appl. mech. engrg., 45, 285-312, (1984) · Zbl 0526.76087
[11] Johnson, C.; Szepessy, A.; Hansbo, P., On the convergence of shock-capturing streamline diffusion finite element methods for conversation laws, Math. comp., 54, 107-129, (1990) · Zbl 0685.65086
[12] Johnson, C.; Johnson, C., The characteristic streamline diffusion method for convection-diffusion problems, (), Mat. apl. comput., 10, (1991)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.