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, issue 1

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 (L2(Ω))2 space, which avoids the use of the classical H(div; Ω) space and reduces the regularity requirement on the gradient solution λ = ∇u. 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 L2 and H1‐norm for both the scalar unknown u and the diffusion term γ and a priori error estimates in (L2) 2‐norm for its gradient λ and its flux σ (the coefficients times the negative gradient). Finally, we provide some numerical results to illustrate the efficiency of our method.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/787891

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:787891

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().