Error estimates for a Galerkin method for a class of model equations for long waves |
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Authors: | Lars Wahlbin |
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Institution: | 1. Dept. of Mathematics White Hall, Cornell University, 14850, Ithaca, N. Y., USA
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Abstract: | 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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