橢圓方程系統的有限元素期後誤差估計

Abstract

在這篇論文中, 我們將有限元素期後誤差估計應用在符合Inf-sup condition 的橢圓系統上.這個誤差估計沒有限定有限元素的次數所以可 以運用在有限元素的h-,p-,hp- 方法上. A general construction technique is presented for a posteriori error estimators of finite element solutions of second order elliptic systems that satisfy the inf-sup conditions. The estimators are obtained by an element-by-element solution of 'weak residual' problems with or without considering element boundary residuals. The local residual problems are exactly in the same form as the original system. There is no order restriction on the finite element spaces used for the approxi- mate solution or the error estimation; that is, the design of the estimators is applicable in connection with either one of the h-, p-, or hp- formulations of the finite element method. Under suitable assumptions the estimators are shown to be bounded by constant multiples of the exact error in suitable norm. A model problem of the liniear elasticity equations is given to illustrate the proposed estimator and to verify necessary conditions for the general theory.