Abstract
The Galerkin method, together with a second order time discretization, is applied to the periodic initial value problem for
. Heref(x, ·) may be highly nonlinear, but a certain cancellation effect is assumed for∫f(x, u) x u. Optimal order error estimates inL 2,H 1, andL ∞ are derived for a general class of piecewise polynomial spaces.
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Wahlbin, L. Error estimates for a Galerkin method for a class of model equations for long waves. Numer. Math. 23, 289–303 (1974). https://doi.org/10.1007/BF01438256
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DOI: https://doi.org/10.1007/BF01438256