Local discontinuous Galerkin methods coupled with implicit integration factor methods for solving reaction-cross-diffusion systems
type: Item
instance of: scholarly article
title: Local discontinuous Galerkin methods coupled with implicit integration factor methods for solving reaction-cross-diffusion systems
zbMATH Open document ID: 1417.65165
DOI: 10.1155/2016/5345032
author: Na An
author: Chaobao Huang
author: Maochang Duan
author: Xijun Yu
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: 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 (\(\Delta t = O(h_{\mathrm{min}}^2)\)), the implicit integration factor (IIF) method is employed for the temporal discretization so that the time step can be relaxed as \(\Delta t = O(h_{\mathrm{min}})\). 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.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K51
zbMATH DE Number: 7026891
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5345032
OpenAlex ID: W2465551786
Wikidata QID: Q59123549
cites work: The chemical basis of morphogenesis
cites work: Existence of Turing instabilities in a two-species fractional reaction-diffusion system
cites work: Turing instabilities in general systems
cites work: Spatial segregation in competitive interaction-diffusion equations
cites work: A mathematical model of plants as ecosystem engineers
cites work: Turing patterns created by cross-diffusion for a Holling II and Leslie-Gower type three species food chain model
cites work: Turing patterns of a strongly coupled predator-prey system with diffusion effects
cites work: An energy-transport model for semiconductors derived from the Boltzmann equation.
cites work: Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering
cites work: A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects
cites work: A Parabolic Cross-Diffusion System for Granular Materials
cites work: Turing instability and traveling fronts for a nonlinear reaction-diffusion system with cross-diffusion
cites work: On nonlinear coupled diffusions in competition systems
cites work: Turing pattern formation in a predator-prey-mutualist system
cites work: A stabilized finite volume element formulation for sedimentation-consolidation processes
cites work: Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion
cites work: Mathematical analysis and numerical simulation of pattern formation under cross-diffusion
cites work: ANALYSIS OF A FINITE VOLUME METHOD FOR A CROSS-DIFFUSION MODEL IN POPULATION DYNAMICS
cites work: Variational multiscale element free Galerkin (VMEFG) and local discontinuous Galerkin (LDG) methods for solving two-dimensional Brusselator reaction-diffusion system with and without cross-diffusion
cites work: The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
cites work: Fourth-Order Time-Stepping for Stiff PDEs
cites work: Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations
cites work: Krylov implicit integration factor methods for spatial discretization on high-dimensional unstructured meshes: application to discontinuous Galerkin methods
cites work: Direct discontinuous Galerkin method for nonlinear reaction-diffusion systems in pattern formation
cites work: Efficient semi-implicit schemes for stiff systems
cites work: Turing Pattern Formation in the Brusselator Model with Superdiffusion
cites work: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
cites work: Q3412614
description: scientific article; zbMATH DE number 7026891