An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems


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.

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N. Chen and H. Gu, "An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems," Applied Mathematics, Vol. 4 No. 4, 2013, pp. 675-679. doi: 10.4236/am.2013.44092.

Conflicts of Interest

The authors declare no conflicts of interest.


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