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• W2964048411 abstract "In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under consideration satisfy five hypotheses. We prove that these five conditions are sufficient for convergence and optimality of the adaptive algorithms under consideration. The main ingredient for the analysis is a new method to analyze both discrete reliability and quasi-orthogonality. This new method arises from an appropriate and natural choice of the norms for both the discrete displacement and stress spaces, namely, a mesh-dependent discrete $H^1$ norm for the former and an $L^2$ norm for the latter, and a newly defined projection operator from the discrete stress space on the coarser mesh onto the discrete divergence free space on the finer mesh. As applications, we prove these five hypotheses for the Raviart--Thomas and Brezzi--Douglas--Marini elements of the Poisson and Stokes problems in both two and three dimensions." @default.
• W2964048411 created "2019-07-30" @default.
• W2964048411 creator A5028500115 @default.
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• W2964048411 date "2018-01-01" @default.
• W2964048411 modified "2023-10-14" @default.
• W2964048411 title "A Unified Analysis of Quasi-Optimal Convergence for Adaptive Mixed Finite Element Methods" @default.
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• W2964048411 doi "https://doi.org/10.1137/16m105513x" @default.
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