典型文献
Maximum-Principle-Preserving Local Discontinuous Galerkin Methods for Allen-Cahn Equations
文献摘要：
In this paper,we study the classical Allen-Cahn equations and investigate the maximum-principle-preserving(MPP)techniques.The Allen-Cahn equation has been widely used in mathematical models for problems in materials science and fluid dynamics.It enjoys the energy stability and the maximum-principle.Moreover,it is well known that the Allen-Cahn equation may yield thin interface layer,and nonuniform meshes might be useful in the numerical solutions.Therefore,we apply the local discontinuous Galerkin(LDG)method due to its flexibility on h-p adaptivity and complex geometry.However,the MPP LDG methods require slope limiters,then the energy stability may not be easy to obtain.In this paper,we only discuss the MPP technique and use numerical experiments to dem-onstrate the energy decay property.Moreover,due to the stiff source given in the equation,we use the conservative modified exponential Runge-Kutta methods and thus can use rela-tively large time step sizes.Thanks to the conservative time integration,the bounds of the unknown function will not decay.Numerical experiments will be given to demonstrate the good performance of the MPP LDG scheme.
文献关键词：
中图分类号：
作者姓名：
Jie Du;Eric Chung;Yang Yang
作者机构：
Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,China;Yanqi Lake Beijing Institute of Mathematical Sciences and Applications,Beijing 101408,China;Department of Mathematics,The Chinese University of Hong Kong,Hong Kong SAR,China;Department of Mathematical Sciences,Michigan Technological University,Houghton,MI 49931,USA
文献出处：
引用格式：
[1]Jie Du;Eric Chung;Yang Yang-.Maximum-Principle-Preserving Local Discontinuous Galerkin Methods for Allen-Cahn Equations)[J].应用数学与计算数学学报,2022(01):353-379
A类：
limiters
B类：
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AB值：
0.582003
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