Based on the splitting in terms of physical processes and with respect to time and on a finite element method (FEM) as applied to a 2D nonlinear vorticity equation, a scheme with two splitting steps is obtained. For constructing FEM operators at the steps of splitting in terms of physical processes, different types of finite elements are used. In the statement of the problem a special attention is given to the depth of a basin. The efficiency of the scheme was tested for a uniform bottom and for the bottom defined by a smooth function.

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