Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional SubdiffusionSuperdiffusion Equations
Joint Authors
Mei, Liquan
Qiu, Meilan
Li, Dewang
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-03-16
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations.
Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively.
Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the L2 norm of the LDG schemes.
Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes.
The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.
American Psychological Association (APA)
Qiu, Meilan& Mei, Liquan& Li, Dewang. 2017. Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional SubdiffusionSuperdiffusion Equations. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-20.
https://search.emarefa.net/detail/BIM-1123190
Modern Language Association (MLA)
Qiu, Meilan…[et al.]. Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional SubdiffusionSuperdiffusion Equations. Advances in Mathematical Physics No. 2017 (2017), pp.1-20.
https://search.emarefa.net/detail/BIM-1123190
American Medical Association (AMA)
Qiu, Meilan& Mei, Liquan& Li, Dewang. Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional SubdiffusionSuperdiffusion Equations. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-20.
https://search.emarefa.net/detail/BIM-1123190
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123190