摘要
目的主要研究了一类半线性二阶抛物型方程在半离散下的非协调有限元法,其中,给定的半线性项f(u)满足Lipschitz条件,探索非协调有限元下真解和离散解的误差估计.方法首先,对所讨论的区域进行正则拟一致剖分,并建立非协调有限元空间.其次,建立半离散非协调有限元的格式.结果借助Riesz投影、一些估计式和Gronwall不等式,得到了L2范数下的真解和离散解之间的收敛速度估计.结论这个结果不仅与h有关,而且还与时间有关,这个结果异于协调有限元下的收敛结果.
Objective In this paper, a class of semi-linear parabolic equations of second order are studied with the methods of nonconforming FEM, where the given term of the semi-linear satisfying the Lipschite conditions, and the error estimations between the real solution and the semi-discrete solution are researched with the FEM. Methods Firstly, the discussed domain is divided into the regular and the quasiconsistent partitions, and then the noncomforming finite element space is established. Secondly, the semi-discrete schemes of the nonconforming FEM are established. Results With the help of Riesz projection, some estimate formula and the gronwall inequality, the convergence rate between the real solution and the corresponding semi-discrete solution under the norm of L2 is obtained. Conclusion Not only does the result relate to h, but also with the time. The result in this paper is different from that of nonconforming FEM.
出处
《河北北方学院学报（自然科学版）》
2009年第1期1-3,8,共4页
Journal of Hebei North University:Natural Science Edition
关键词
抛物型方程
半线性
半离散
非协调有限元
收敛速度
parabolic equation
semi-linear
semi-discrete
nonconforming FEM
convergence rate
