TITLE:
An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems
AUTHORS:
Ning Chen, Haiming Gu
KEYWORDS:
Adaptive Method; Least-Squares Mixed Finite Element Method; Fourth Order Parabolic Problems; Least-Squares Functional; A Posteriori Error
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.4,
April
29,
2013
ABSTRACT: A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.