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On convergence of the finite element method for the wave equation. (English) Zbl 0575.65091

For the semidiscrete, piecewise linear Galerkin approximation of the periodic initial value problem (with initial values f(x)) of the one- dimensional wave equation the author shows that \(f\in H^ 3\) is necessay for second order accuracy, instead of the plausible \(f\in H^ 2\). A similar result holds for the usual semidiscrete difference scheme. It is also shown that second order accuracy for \(f\in H^ 2\) can be obtained if \(f_ n\to 0\) sufficiently fast with increasing n, for the Fourier coefficients \(f_ n\) of f.
Reviewer: G.Stoyan

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
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