A second order explicit finite element scheme to multi-dimensional conservation laws and its convergence

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 43, Issue 9, 2000, Pages 945-957

  Ying, Long'an ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Conservation law; Convergence; Finite element method

Indexed keywords

EID: 0043262761     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02879800     Document Type: Article

References (8)

1. Kröner, D., Rokyta, M., Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions, SIAM J. Numer. Anal., 1994, 31: 324.
2. Johnson, C., Szepessy, A., On the convergence of a finite element method for a nonlinear hyperbolic conservation law, Math. Comp., 1987, 49: 427.
3. Cockburn, B., Shu, C. -W., TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Math. Comp., 1989, 52: 411.
4. Xu, J., Ying, L. -A., Convergence of an explicit upwind finite element method to multi-dimensional conservation laws, J. Comp. Math, (to appear).
5. Xu, J., Zikatanov, L., A monotone finite element scheme for convection-diffusion equations, Math. Comp., 1999, 68: 1429.
6. Ciarlet, P. G., The Finite Element Method for Elliptic Problems, Amsterdam: North-Holland, 1978.
7. DiPerna, R. J., Measure-valued solutions to conservation laws, Arch. Rat. Mech. Anal., 1985, 88: 223.
8. Zhou, A., Lin, Q., Optimal and superconvergence estimates of the finite element method for a scalar hyperbolic equation, Acta Mathematica Scientia, 1994, 14(1): 90.