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

Archer, David; Díaz, Julio César

doi:10.1090/S0025-5718-1982-0637285-X

A collocation-Galerkin method for a first order hyperbolic equation with space and time dependent coefficient
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by David Archer and Julio César Díaz PDF

Math. Comp. 38 (1982), 37-53 Request permission

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 $r - 1$ on [0, 1] with respect to the weight function $x(1 - x)$. Optimal ${L^\infty }({L^2})$-norm estimates of the error are derived.

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