Acta mathematica scientia,Series B ›› 1993, Vol. 13 ›› Issue (3): 335-349.
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Shen Shumin, Deng Qingping
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Abstract: This paper deals with maximum norm error estimates of conforming finite element approximate solutions for the stationary and nonstationary Navier-Stokes problems in a plane bounded domain, using the so-called velocity-pressure mixed variational formulation. Quasi-optimal maximum norm error estimates of the velocity and its first derivatives, and the pressure are obtained for conforming finite element approximations of the stationary Navier-Stokes problem by some estimates of the Green function and their finite element approximations for Stokes problem. Moreover, with the method of Navier-Stokes projection, quasi-optimal maximum norm error estimate results are shown for semidiscrete conforming finite element approximations of the nonstationary Navier-Stokes problem.
Shen Shumin, Deng Qingping. MAXIMUM NORM ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE STATIONARY AND NONSTATIONARY NAVIER-STOKES PROBLEMS[J].Acta mathematica scientia,Series B, 1993, 13(3): 335-349.
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