Adaptive Finite Element Methods For Elliptic Eigenvalue Problem

Adaptive finite element methods (AFEM) have been widely used to solve thescientific problems governed by partial di?erential equations (PDE). The generalidea is to achieve better accuracy with minimum degree of freedom. A e?ectiveposteriori error estimator is the basis of designing the AFEM and the posteriorierror estimator provides the good information of the approximation error to refinethe mesh. So a posteriori error estimates has become a central theme in the AFEM.In this paper, We consider AFEM for elliptic eigenvalue problem. We use twoposteriori error estimates methods to solve the problems, one is the superconvergentcluster recovery (SCR) method, the other is explicit polynomial recovery (EPR)method. SCR is relatively simple to implement, cheap in term of computationalcost. This new gradient recovery method will be considered to be applied to ellipticeigenvalue problem to enhance eigenvalue approximation. EPR is simple and wecan easily understand it, the computational cost of it is also small. The experimentsexplain that the two posteriori error estimates methods in this thesis are useful, andwe can achieve the optimal complexity about the AFEM.