A superconvergent nonconforming mixed finite element method for the  N avier– S tokes equations | Zendy

Ren Jincheng | Zendy; Ma Yue | Zendy

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A superconvergent nonconforming mixed finite element method for the N avier– S tokes equations

Author(s) -

Ren Jincheng,

Ma Yue

Publication year - 2016

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22023

Subject(s) - superconvergence , mathematics , piecewise , finite element method , norm (philosophy) , mathematical analysis , mixed finite element method , partial differential equation , constant (computer programming) , stokes problem , physics , computer science , political science , law , thermodynamics , programming language

The superconvergence for a nonconforming mixed finite element approximation of the Navier–Stokes equations is analyzed in this article. The velocity field is approximated by the constrained nonconforming rotated Q 1 (CNR Q 1 ) element, and the pressure is approximated by the piecewise constant functions. Under some regularity assumptions, the superconvergence estimates for both the velocity in broken H 1 ‐norm and the pressure in L 2 ‐norm are obtained. Some numerical examples are presented to demonstrate our theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 646–660, 2016

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