Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A finite element method for time-dependent convection-diffusion equations

Author: Gerard R. Richter
Journal: Math. Comp. 54 (1990), 81-106
MSC: Primary 65N30; Secondary 76-08, 76Rxx
MathSciNet review: 993932
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present a finite element method for time-dependent convection-diffusion equations. The method is explicit and is applicable with piecewise polynomials of degree $ n \geq 2$. In the limit of zero diffusion, it reduces to a recently analyzed finite element method for hyperbolic equations. Near optimal error estimates are derived. Numerical results are given.

References [Enhancements On Off] (What's this?)

  • [1] 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 881364 (88d:65133)
  • [2] C. Johnson, U. Nävert, and J. Pitkäranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 45 (1984), 285-312. MR 759811 (86a:65103)
  • [3] C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp. 46 (1986), 1-26. MR 815828 (88b:65109)
  • [4] P. Lesaint and P. A. Raviart, On a finite element method for solving the neutron transport equation, Mathematical Aspects of Finite Elements in Partial Differential Equations (C. deBoor, ed.), Academic Press, 1974, pp. 89-123. MR 0658142 (58:31918)
  • [5] U. Nävert, A finite element method for convection-diffusion problems, Ph. D. thesis, Dept. of Computer Sciences, Chalmers Inst. of Tech., Göteborg, 1982.
  • [6] W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory Report LA-UR-73-479, 1973.
  • [7] G. R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp. 50 (1988), 75-88. MR 917819 (88j:65197)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 76-08, 76Rxx

Retrieve articles in all journals with MSC: 65N30, 76-08, 76Rxx

Additional Information

Keywords: Finite element, hyperbolic
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society