带有阻尼项的定常Stokes方程的低阶非协调混合有限元方法的超逼近和超收敛分析

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Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary
Stokes Equations with Damping

Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary Stokes Equations with Damping

Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary
Stokes Equations with Damping

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Abstract:

In this paper, we apply the constrained nonconforming rotated Q₁element and the piecewise constant element to approximate the velocity and the pressure for the stationary、impressible Stokes equations with damped term, respectively. The existence and uniqueness of the approximated solutions are proved. Employing the prior estimates of the exact and approximate solutions and choosing the appropriate parameters α, ν and r, the optimal error estimates and the superclose results are derived. Finally, the O(h²) order global superconvergence in H¹-norm for the velocity and L²-norm for the pressure is obtained by use of a postprocessing technique.

Key words: Stokes equations, Damped term, Nonconforming mixed elements, Superclose and superconvergence, Optimal error estimates

CLC Number:

65N30

SHI Dong-Yang, YU Zhi-Yun. Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary
Stokes Equations with Damping[J].Acta mathematica scientia,Series A, 2013, 33(4): 735-745.

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