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

Yang Liu, Hong Li, Zhichao Fang, Siriguleng He and Jinfeng Wang

Advances in Mathematical Physics, 2013, vol. 2013, 1-14

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:787891

DOI: 10.1155/2013/787891

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