Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods  

作　　者：Luoping Chen Yanping Chen 

机构地区：[1]School of Mathematic,Southwest Jiaotong University,Chengdu 611756,P.R.China [2]School of Mathematic science,South China Normal University,Guangzhou 510631,P.R.China

出　　处：《Advances in Applied Mathematics and Mechanics》2014年第2期203-219,共17页应用数学与力学进展（英文）

基　　金：National Science Foundation of China(11271145);Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009);the Project of Department of Education of Guangdong Province(2012KJCX0036).

摘　　要：In this paper,we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods.We mainly concern the case when pressure coefficients and source terms are nonlinear.To linearize the nonlinear mixed equations,we use the two-grid algorithm.We first solve the nonlinear equations on the coarse grid,then,on the fine mesh,we solve a linearized problem using Newton iteration once.It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h 1/2).As a result,solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.

关 键 词：Two-grid method reaction-diffusion equations mixed finite element methods. 

分 类 号：O17[理学—数学]