非稳态四阶椭圆方程的Galerkin有限元法  

Finite Element Method for Fourth Order Nonstationary Elliptic Equation

作　　者：戴培良[1] 戴嘉尊[1] 

机构地区：[1]南京航空航天大学理学院

出　　处：《南京航空航天大学学报》2002年第1期27-30,共4页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：江苏省教育厅自然科学基金 (编号 :OOSJD1 1 0 0 0 8)资助项目

摘　　要：针对平面有界凸多角形区域上一类非稳态四阶椭圆方程 u t+Δ2 u =f (x,t) (x,t)∈Ω× [0 ,T]u = u n=0 (x,t)∈ Ω× [0 ,T]u(x,0 ) =u0 (x) x∈Ω的初边值问题进行了 Galerkin有限元方法分析。首先给出了所讨论问题的 Galerkin有限元方法的离散格式 ,其次对所讨论问题的解与其离散问题的解之间的误差进行了分析研究 ,最后利用椭圆投影算子的性质 。Galerkin finite element methods for an initial boundary value problem of a fourth order nonstationary elliptic equation in two dimension space are treated. The problem is[HL(2:1,2Z;2,1Z]ut+Δ 2u=f(x,t)(x,t)∈Ω× u=un=0(x,t)∈Ω× u(x,0)=u 0(x)x∈ΩFirstly, this paper studies the discrete approximation scheme of the Galerkin finite element methods for the above discussed problem. Secondly, the error estimates for the solution of the problem and the solution of the discrete approximation scheme are considered. Finally, by means of the elliptic projection operator, some error estimates in a certain norm are derived.

关 键 词：非稳态四阶椭圆方程 GALERKIN有限元法 误差估计 离散格式 

分 类 号：O241.82[理学—计算数学]