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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the convergence of Galerkin approximation schemes for second-order hyperbolic equations in energy and negative norms
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by Tunc Geveci PDF
Math. Comp. 42 (1984), 393-415 Request permission

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.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 393-415
  • MSC: Primary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0736443-5
  • MathSciNet review: 736443