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Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems
Joint Authors
An, Na
Yu, Xijun
Huang, Chaobao
Duan, Maochang
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-06-29
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences.
The two-dimensional system is discretized by the local discontinuous Galerkin (LDG) method on unstructured triangular meshes associated with the piecewise linear finite element spaces, which can derive not only numerical solutions but also approximations for fluxes at the same time comparing with most of study work up to now which has derived numerical solutions only.
Considering the stability requirement for the explicit scheme with strict time step restriction ( Δ t = O ( h m i n 2 ) ), the implicit integration factor (IIF) method is employed for the temporal discretization so that the time step can be relaxed as Δ t = O ( h m i n ) .
Moreover, the method allows us to compute element by element and avoids solving a global system of nonlinear algebraic equations as the standard implicit schemes do, which can reduce the computational cost greatly.
Numerical simulations about the system with exact solution and the Brusselator model, which is a theoretical model for a type of autocatalytic chemical reaction, are conducted to confirm the expected accuracy, efficiency, and advantages of the proposed schemes.
American Psychological Association (APA)
An, Na& Yu, Xijun& Huang, Chaobao& Duan, Maochang. 2016. Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1103484
Modern Language Association (MLA)
An, Na…[et al.]. Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-18.
https://search.emarefa.net/detail/BIM-1103484
American Medical Association (AMA)
An, Na& Yu, Xijun& Huang, Chaobao& Duan, Maochang. Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-18.
https://search.emarefa.net/detail/BIM-1103484
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103484