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Mathematics of Computation

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The convergence of Galerkin approximation schemes for second-order hyperbolic equations with dissipation

Authors: Barbara Kok and Tunc Geveci
Journal: Math. Comp. 44 (1985), 379-390, S17
MSC: Primary 65M10; Secondary 65M60
MathSciNet review: 777270
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Abstract: In this paper we consider certain semidiscrete and fully discrete Galerkin approximations to the solution of an initial-boundary value problem for a second-order hyperbolic equation with a dissipative term. Estimates are obtained in the energy and negative norms associated with the problem, yielding in particular $ {H^1}$- and $ {L^2}$-error estimates. The approximation to the initial data is taken, in this case, as the projection with respect to the energy inner product, onto the approximating space. We also obtain estimates for higher-order time derivatives.

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Article copyright: © Copyright 1985 American Mathematical Society

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