Rauch, Jeffrey On convergence of the finite element method for the wave equation. (English) Zbl 0575.65091 SIAM J. Numer. Anal. 22, 245-249 (1985). 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 Cited in 1 ReviewCited in 26 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35L05 Wave equation Keywords:Galerkin method; rate of convergence; extra derivative of regularity × Cite Format Result Cite Review PDF Full Text: DOI