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The Crank-Nicolson Extrapolation Stabilized Finite Element Method for Natural Convection Problem

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  • Yunzhang Zhang
  • Yanren Hou

Abstract

This paper studies a fully discrete Crank-Nicolson linear extrapolation stabilized finite element method for the natural convection problem, which is unconditionally stable and has second order temporal accuracy of . A simple artificial viscosity stabilized of the linear system for the approximation of the new time level connected to antidiffusion of its effects at the old time level is used. An unconditionally stability and an a priori error estimate are derived for the fully discrete scheme. A series of numerical results are presented that validate our theoretical findings.

Suggested Citation

  • Yunzhang Zhang & Yanren Hou, 2014. "The Crank-Nicolson Extrapolation Stabilized Finite Element Method for Natural Convection Problem," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-22, May.
    • Handle: RePEc:hin:jnlmpe:393494
    DOI: 10.1155/2014/393494
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