A finite element method for time-dependent convection-diffusion equations
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- by Gerard R. Richter PDF
- Math. Comp. 54 (1990), 81-106 Request permission
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
- Richard S. Falk and Gerard R. Richter, Analysis of a continuous finite element method for hyperbolic equations, SIAM J. Numer. Anal. 24 (1987), no. 2, 257–278. MR 881364, DOI 10.1137/0724021
- Claes Johnson, Uno Nävert, and Juhani Pitkäranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 45 (1984), no. 1-3, 285–312. MR 759811, DOI 10.1016/0045-7825(84)90158-0
- C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp. 46 (1986), no. 173, 1–26. MR 815828, DOI 10.1090/S0025-5718-1986-0815828-4
- P. Lasaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation, Mathematical aspects of finite elements in partial differential equations (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974) Publication No. 33, Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, pp. 89–123. MR 0658142 U. Nävert, A finite element method for convection-diffusion problems, Ph. D. thesis, Dept. of Computer Sciences, Chalmers Inst. of Tech., Göteborg, 1982. 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.
- Gerard R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp. 50 (1988), no. 181, 75–88. MR 917819, DOI 10.1090/S0025-5718-1988-0917819-3
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Math. Comp. 54 (1990), 81-106
- MSC: Primary 65N30; Secondary 76-08, 76Rxx
- DOI: https://doi.org/10.1090/S0025-5718-1990-0993932-9
- MathSciNet review: 993932