OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Abstract

Abstract:

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Key words: Navier-Stokes equation, Darcy's law, two-grid method, optimal error estimate

Yi QIN, Yanren HOU. OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL[J].Acta mathematica scientia,Series B, 2018, 38(4): 1361-1369.

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