A Posterior Error Estimator Of Least-squares Mixed Method For Parabolic Problems

In this paper,we propose a least-squares mixed element procedure for the fully discrete scheme approximate solution to the parabolic equations.By selecting the least-squares functional properly,the resulting procedure can be split into two independent symmetric positive definite schemes,one of which is for the field variable and the other of which is for the flux variable.Thus we can respectively give a posterior error estimation of the corresponding approximation solutions on each of their solution spaces.As a result ,on each discrete time layer,kinds of a posterior error estimation method for elliptic equations can be used.And in this paper we make a use of a residual type subdomain-based flux-free a posterior error estimator ,which has a higher efficiency and well accuracy.It estimates upper and lower bounds of the error in energy norm.In the procedure of computing the a posteriori estimation,the boundry conditions of the local problems are trivial and the usual data structure of a finite element code is directly employed.Thus computational efficiency is improved.