对散度—旋度系统三类不同有限元法数值试验的比较

本文对散度-旋度系统给出了三类不同的有限元法,即最小二乘法,惩罚法和子域配置/最小二乘法。数值试验与理论分析得到的收敛阶一致。‖e‖_1≤ch_1,‖e‖_0≤C_2h~2只是常数C略有不同。上列方法也可用于一般一阶线性椭圆方程组的正则边值问题.

COMPARISON OF NUMERICAL EXPERIMENTS FOR THE DIV CURL SYSTEM BY THREE DIFFERENT FINITE ELEMENT METHODS

In this paper we give three kinds of different flnite element methods for the div-curl system,i.e., the least squares method 1,2,3],the penalized method 4],and the subdomain collocation/least squares method 5].All of the numerical material supports the degrees of convergence obtained by theoretical analysis.These are ‖e‖_1≤c_1h and‖e‖_0≤c_2h~2,but the constants,C's are slightly different.On the other hand,the general methods of first order linear systems will be derived and the theorems concerning the convergence will be reviewed.