In this work we describe one of the methods of constructing approximate hydrodynamic models with the supposition of a long wave nature of flow. This method allows us to derive a nonlinear dispersive model to obtain its variational wording. We consider the general case of hydrodynamic equations for a potential ideal fluid flow over an irregular bottom as well as some special cases.
We consider the Galerkin piecewise linear finite element method for an ordinary convectiondiffusion boundary value problem with a small parameter in front of the highest derivative. For the generation of a discrete linear algebraic System we use the special quadrature formulae that take into account the boundary layer character of the solution. It is proved that the resulting discrete problem is of ε 2 + Λ 2 -Order of accuracy in the uniform discrete norm for small h and ε. The numerical example shows the advantage of the considered discrete scheine over two commonly used difference schemes.'Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk 660036, Russia
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