A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

doi:10.1016/S0252-9602(15)30039-4

Abstract

Abstract:

A time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element (SCNMFVE) formulation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

Key words: non-stationary parabolized Navier-Stokes equations, stabilized Crank-Nicolson mixed finite volume element formulation, error estimate

CLC Number:

65N12

Zhendong LUO. A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS[J].Acta mathematica scientia,Series B, 2015, 35(5): 1055-1066.

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