非线性抛物问题的二重网格混合元算法  

A Two-grid Algorithm for Mixed Finite Element Solution of Nonlinear Parabolic Equations

作　　者：刘伟[1] 芮洪兴[2] 龙晓翰[1] 

机构地区：[1]鲁东大学数学与信息学院,烟台264025 [2]山东大学数学与系统科学学院,济南250100

出　　处：《应用数学学报》2007年第4期635-643,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10471079号);博士点基金(20060422006号)资助项目.

摘　　要：针对一类非线性抛物方程的混合元形式,本文提出了二重网格算法.该算法是在网格大小为H的粗网格上求解—个非线性系统,再在网格大小为h的细网格上进行两次线性计算.算法第二步和第三步的误差分别为O(△_t^2+h^(k+1)+H^(2K+2)),O(△_t^2+h^(k+1)+h^(-d/2)H^(4k+4)),其中k为逼近空间的多项式的次数,d为空间维数.该估计对H的选取起了很大的作用.对于粗网格上的非线性计算,本文给出了L^p(2≤p<∞)模误差估计.A two-grid algorithm for mixed finite element solution of nonlinear parabolic equations is presented in this paper. The algorithm involves solving one small nonlinear problem on the coarse grid of size H and two linear problems on the fine grid of size h. Error estimates are derived which demonstrate that the error is O（△t^2＋h^（k＋1）＋H^（2k＋1）,O（△t^2＋h^（k＋1）＋h^（-d/2）H^（4k＋4）, where k is the degree of the approximating space for the primary variable and d is spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problem. The error estimate in L^p for the nonlinear solution of the coarse grid is also presented.

关 键 词：混合元 非线性抛物方程 二重网格法 

分 类 号：O241.82[理学—计算数学]