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An Adaptive Least-Squares Mixed Finite Element Method for Fourth Order Parabolic Problems
Department of Mathematics, Qingdao University of Science and Technology, Qingdao, China
Department of Mathematics, Qingdao University of Science and Technology, Qingdao, China
- 1 Department of Mathematics, Qingdao University of Science and Technology, Qingdao, China
- 2 Department of Mathematics, Qingdao University of Science and Technology, Qingdao, China
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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.
KeywordsAdaptive MethodLeast-Squares Mixed Finite Element MethodFourth Order Parabolic ProblemsLeast-Squares Functional<i>A</i><i>Posteriori</i>Error
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