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Error estimates for a Galerkin method for a class of model equations for long waves

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The Galerkin method, together with a second order time discretization, is applied to the periodic initial value problem for

$$\frac{\partial }{{\partial t}}(u - (a(x)u_x )_x ) + (f(x,u))_x = 0$$

. 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).

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