Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the convergence of Galerkin approximation schemes for second-order hyperbolic equations in energy and negative norms

Author: Tunc Geveci
Journal: Math. Comp. 42 (1984), 393-415
MSC: Primary 65M60
MathSciNet review: 736443
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given certain semidiscrete and single step fully discrete Galerkin approximations to the solution of an initial-boundary value problem for a second-order hyperbolic equation, ${H^1}$ and ${L^2}$ error estimates are obtained. These estimates are valid simultaneously when the approximation to the initial data is taken to be the projection onto the approximating space with respect to the inner product which induces the energy norm that is naturally associated with the problem. The ${L^2}$-estimate is obtained as a by-product of the analysis of convergence in certain negative norms. Estimates are also obtained for the convergence of higher-order time derivatives in the presence of sufficiently smooth data.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M60

Retrieve articles in all journals with MSC: 65M60

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society