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A Coupling Method of New EMFE and FE for Fourth-Order Partial Differential Equation of Parabolic Type

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  • Yang Liu
  • Hong Li
  • Zhichao Fang
  • Siriguleng He
  • Jinfeng Wang

Abstract

We propose and analyze a new numerical method, called a coupling method based on a new expanded mixed finite element (EMFE) and finite element (FE), for fourth-order partial differential equation of parabolic type. We first reduce the fourth-order parabolic equation to a coupled system of second-order equations and then solve a second-order equation by FE method and approximate the other one by a new EMFE method. We find that the new EMFE method’s gradient belongs to the simple square integrable space, which avoids the use of the classical H (div; Ω) space and reduces the regularity requirement on the gradient solution . For a priori error estimates based on both semidiscrete and fully discrete schemes, we introduce a new expanded mixed projection and some important lemmas. We derive the optimal a priori error estimates in and -norm for both the scalar unknown and the diffusion term γ and a priori error estimates in -norm for its gradient and its flux (the coefficients times the negative gradient). Finally, we provide some numerical results to illustrate the efficiency of our method.

Suggested Citation

  • Yang Liu & Hong Li & Zhichao Fang & Siriguleng He & Jinfeng Wang, 2013. "A Coupling Method of New EMFE and FE for Fourth-Order Partial Differential Equation of Parabolic Type," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-14, April.
  • Handle: RePEc:hin:jnlamp:787891
    DOI: 10.1155/2013/787891
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