Abstract: The author provides a new discretization method-the finite volume method(FVM). For the Stokes equation the velocity space is approximated by the nonconforming linear element based on the dual partition and the pressure by the piecewise constant based on the primal triangulation. Under the suitable smoothness of the solution, the optimal convergence rate O(h) is obtained, where h denotes the parameter of the space discretization.

Key words: Stokes equation, finite volume method, Crouzeix-Raviart element

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