A collocation-Galerkin method for a first order hyperbolic equation with space and time dependent coefficient

Authors:
David Archer and Julio César Díaz

Journal:
Math. Comp. **38** (1982), 37-53

MSC:
Primary 65M60; Secondary 65N35

MathSciNet review:
637285

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree on [0, 1] with respect to the weight function . Optimal -norm estimates of the error are derived.

**[1]**David Archer,*Collocation in 𝐶⁰ spaces for first order hyperbolic equations. I. Optimal order global estimates for quasilinear problems*, SIAM J. Numer. Anal.**15**(1978), no. 2, 271–281. MR**0474889****[2]**Garth A. Baker,*A finite element method for first order hyperbolic equations*, Math. Comput.**29**(1975), no. 132, 995–1006. MR**0400744**, 10.1090/S0025-5718-1975-0400744-5**[3]**J. C. Diaz Velasco, Ph. D. Thesis, Rice University, Houston, Texas, 1974.**[4]**Julio César Díaz,*A collocation-Galerkin method for the two point boundary value problem using continuous piecewise polynomial spaces*, SIAM J. Numer. Anal.**14**(1977), no. 5, 844–858. MR**0483480****[5]**Julio César Díaz,*Collocation-𝐻⁻¹-Galerkin method for parabolic problems with time-dependent coefficients*, SIAM J. Numer. Anal.**16**(1979), no. 6, 911–922. MR**551315**, 10.1137/0716067**[6]**Roderick J. Dunn Jr. and Mary Fanett Wheeler,*Some collocation-Galerkin methods for two-point boundary value problems*, SIAM J. Numer. Anal.**13**(1976), no. 5, 720–733. MR**0433896****[7]**Mary Fanett Wheeler,*An elliptic collocation-finite element method with interior penalties*, SIAM J. Numer. Anal.**15**(1978), no. 1, 152–161. MR**0471383**

Retrieve articles in *Mathematics of Computation*
with MSC:
65M60,
65N35

Retrieve articles in all journals with MSC: 65M60, 65N35

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637285-X

Article copyright:
© Copyright 1982
American Mathematical Society