A finite element method for first order hyperbolic equations

Author:
Garth A. Baker

Journal:
Math. Comp. **29** (1975), 995-1006

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1975-0400744-5

MathSciNet review:
0400744

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Abstract: A class of finite element methods is proposed for first order hyperbolic equations. The expository example chosen is of a single equation in one space dimension with constant coefficients.

Optimal error estimates are derived for both approximations continuous in the time variable and an approximation scheme discrete in time.

**[1]**I. BABUŠKA, "Error-bounds for finite element method,"*Numer. Math.*, v. 16, 1970/71, pp. 322-333. MR**44**#6166. MR**0288971 (44:6166)****[2]**J. H. BRAMBLE & V. THOMÉE,*Discrete Time Galerkin Methods for a Parabolic Boundary Value Problem*, MRC Tech. Report #1240, University of Wisconsin, 1972.**[3]**J. DOUGLAS, JR. & T. DUPONT, "Galerkin methods for parabolic equations,"*SIAM J. Numer. Anal.*, v. 7, 1970, pp. 575-626. MR**43**#2863. MR**0277126 (43:2863)****[4]**J. L. LIONS & E. MAGENES,*Non-Homogeneous Boundary Value Problems and Applications*. Vol. I, Springer-Verlag, New York, 1972. MR**0350177 (50:2670)****[5]**H. H. RACHFORD, JR. & M. F. WHEELER, " Galerkin procedure for the two point boundary value problem,"*Mathematical Aspects of the Finite Element Method*, C. DeBoor (Editor), Academic Press, New York, 1974. MR**0349031 (50:1525)****[6]**M. SCHECTER. "On estimates and regularity. II,"*Math. Scand.*, v. 13, 1963, pp. 47-69. MR**32**#6052. MR**0188616 (32:6052)****[7]**M. F. WHEELER, "A priori error estimates for Galerkin approximations to parabolic partial differential equations,"*SIAM J. Numer. Anal.*, v. 10, 1973, pp. 723-759. MR**0351124 (50:3613)**

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DOI:
https://doi.org/10.1090/S0025-5718-1975-0400744-5

Article copyright:
© Copyright 1975
American Mathematical Society