Fully discrete local discontinuous Galerkin methods for some time-fractional fourth-order problems

Abstract

In this paper, we study the local discontinuous Galerkin (LDG) method for some time-fractional fourth-order differential equations. The method was recently employed to solve the problem and shown to converge with order $O({\tau }^{-\alpha }{h}^{k+1}+{\tau }^{2-\alpha }+{\tau }^{-\alpha /2}{h}^{k+1/2}+h^{k+1})$. We find that the LDG method can actually achieve convergence rate equals $O({\tau }^{2-\alpha }+h^{k+1})$. The claims are justified by numerical tests.

Keywords:

• local discontinuous Galerkin method
• time-fractional fourth-order equations
• stability
• convergence

2010 AMS Subject Classifications:

• 35R11
• 65M12
• 65M15
• 65M60

Acknowledgments

The authors would like to express their gratitude to the editor and the referees for their valuable suggestions, which help to improve the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This author is supported by the Macao Science and Technology Development Fund (FDCT) [001/2013/A] and the grant [MYRG2015-00064-FST] from University of Macau.