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Equal-order discontinuous finite volume element methods for the Stokes problem

The aim of this paper is to develop and analyze a one-parameter family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element (FE) approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. {\it A priori} error estimates are derived for the velocity and pressure in the mesh-dependent norm, and optimal convergence rates are predicted for velocity in the $L^2-$norm under the assumption that source term is locally in $ H^1$. Several numerical experiments are presented to validate the theoretical findings.

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