A continuous space-time finite element method for the wave equation

Mathematics of Computation

Volumn 65, Issue 214, 1996, Pages 491-506

  French, Donald A ^a   Peterson, Todd E ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION BY FUNCTION; CONTINUOUS FUNCTION; DISCRETIZATION; ENERGY METHOD; ERROR ESTIMATION; SPACE TIME; TENSOR PRODUCT; WAVE EQUATION;

CONVERGENCE OF NUMERICAL METHODS; VARIATIONAL TECHNIQUES;

FINITE ELEMENT METHOD;

EID: 0030376796     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-96-00685-0     Document Type: Article

References (18)

1. A. K. Aziz and P. Monk, Continuous finite elements in space and time for the heat equation, Math. Comp. 52 (1989), 255-2T4. MR 90d:65189
2. I. Babuška and T. Janik, The h-p version of the finite element method, SIAM J. Numer. Anal. 5 (1990), 363-399.
3. G. A. Baker and J. H. Bramble, Semidiscrete and single step fully discrete approximations for second order hyperbolic equations, RAIRO Anal. Numér. 13 (1979), 75-100. MR 80f:65115
4. L. Bales and I. Lasiecka, Continuous finite elements in space and time for the nonhomogeneous wave equation, Comput. Math. Appl. 27 (1994), 91-102. MR 94k:65138
5. 2 Dirichlet boundary data, Math. Comp. 64 (1995), 89-115. MR 95c:65176
6. J. L. Bona, V. A. Dougalis, and O. A. Karakashian, Fully discrete Galerkin methods for the Korteweg-de Vries equation, Comput. Math. Appl. 12A (1986), 859-884. MR 87j:65108
7. J. DeFrutos and J. M. Sanz-Serna, Accuracy and conservation properties in numerical integration: the case of the Korteweg-deVries equation, preprint.
8. R. S. Falk and G. R. Richter, Analysis of a continuous finite element method for hyperbolic equations, SIAM J. Numer. Anal. 24 (1987), 257-278. MR 88d:65133
9. D. A. French and S. Jensen, Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems. IMA J. Numer. Anal. 14 (1994), 421-442. MR 95d:65083
10. D. A. French and T. E. Peterson, A space-time finite element method for the second order wave equation, Report CMA-MR13-91, Centre for Mathematics and its Applications, Canberra.
11. D. A. French and J. W. Schaeffer, Continuous finite element methods which preserve energy properties for nonlinear problems, Appl. Math. Comput. 39 (1991), 271-295. MR 91i:65165
12. R. T. Glassey, Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension, Math. Comp. 58 (1992), 83-102. MR 92e:65123
13. R. T. Glassey and J. Schaeffer, Convergence of a second-order scheme for semilinear hyperbolic equations in 2 + 1 dimensions, Math. Comp. 56 (1991), 87-106. MR 92h:65140
14. C. Johnson, Discontinuous Galerkin finite element methods for second order hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 107 (1993), 117-129. MR 95c:65154
15. O. Karakashian, G. D. Akrivis, and V. A. Dougalis, On optimal order error estimates for the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 30 (1993), 377-400. MR 94c:65119
16. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983. MR 85g:47061
17. G. R. Richter, An explicit finite element method for the wave equation, preprint.
18. W. Strauss and L. Vazquez Numerical solution of a nonlinear Klein-Gordon equation, J. Comput. Phys. 28 (1978), 271-278. MR 58:19970