A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations. (16th August 2016)

• Record Type: Journal Article
• Authors: Yang, Suxiang; Chen, Huanzhen
• Other Names: Mei Ming Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2016(2016)
• Publication Date: 2016-08-16
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2016/9398265
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. The appearance of the singular term in the solution leads to lower regularity of the solution of the equation, so to the lower order convergence rate for the numerical solution. In this paper, by the dividing of equation, we drop the lower regularity term in the solution successfully and get a new fractional elliptic equation which has full regularity. We present a theoretical framework of mixed finite element approximation to the new fractional elliptic equation and derive the error estimates for unknown function, its derivative, and fractional-order flux. Some numerical results are illustrated to confirm the optimal error estimates.