自适应有限元方法在线性椭圆方程的应用

ADAPTIVE FINITE ELEMENT METHOD FOR LINEN ELLIPTIC PROBLEMS

本文完整给出在凸多边形域上关于Ｐｏｉｓｓｏｎ方程的先验及后验误差估计及基于后验误差估计的自适应有限元方法，从理论上证明了这种自动误差控制的方法是可靠的，有效的。

A posteriori and a priori error estimates are derived for a finite element discretization of poissons equations on convex polygonal demains.The algorithem that we constructed for the automatic coutrol of error is both reliable and efficient.The adaptive algorithem is based on the a posteriori error estimate which proves reliability and sharp the a priori error estimates are used to prove efficienty.Some numerical computations illustrate the theoretical results.