A finite element method for first order hyperbolic equations

Author:
Garth A. Baker

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

MSC:
Primary 65N30

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]**Ivo Babuška,*Error-bounds for finite element method*, Numer. Math.**16**(1970/1971), 322–333. MR**0288971****[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]**Jim Douglas Jr. and Todd Dupont,*Galerkin methods for parabolic equations*, SIAM J. Numer. Anal.**7**(1970), 575–626. MR**0277126****[4]**J.-L. Lions and E. Magenes,*Non-homogeneous boundary value problems and applications. Vol. I*, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth; Die Grundlehren der mathematischen Wissenschaften, Band 181. MR**0350177****[5]**Carl de Boor (ed.),*Mathematical aspects of finite elements in partial differential equations*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Publication No. 33 of the Mathematics Research Center, The University of Wisconsin-Madison. MR**0349031****[6]**Martin Schechter,*On 𝐿^{𝑝} estimates and regularity. II*, Math. Scand.**13**(1963), 47–69. MR**0188616****[7]**Mary Fanett Wheeler,*A priori 𝐿₂ error estimates for Galerkin approximations to parabolic partial differential equations*, SIAM J. Numer. Anal.**10**(1973), 723–759. MR**0351124**

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

Article copyright:
© Copyright 1975
American Mathematical Society