Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity
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For the planar elasticity equation, we prove the uniform convergence and optimality of an adaptive mixed method using the hybridized mixed finite element in [Numer. Math., 141 (2019), pp. 569-604] proposed by Gong, Wu, and Xu. The main ingredients of the proof consist of the discrete reliability and quasi-orthogonality, which are both derived using a discrete approximation result. Compared with Arnold--Winther and Hu--Zhang mixed elements, the adaptive hybridized mixed method yields nested discrete stress spaces so that the rigorous quasi-optimal convergence rate can be established.
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