A Priori Analysis for the Semi{discrete Approximation to the Nonlinear Damped Wave Equation
نویسنده
چکیده
We study the second{order nonlinear damped wave equation semi{discretised in space using standard Galerkin nite element methods. Denoting the analytical solution and the corresponding nite element solution to the given problem by u and u h respectively, we derive an optimal L 2 (() error estimate of the form max t20;T] ku (t) ? u h (t)k C (u) h m ; for (x; t) 2 0; T], where R d ; C is a positive constant depending on u, h is the grid parameter, and m > 1 + d=2, where m ? 1 is the degree of the piecewise polynomials in the nite element test space.
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تاریخ انتشار 1999