Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors

07/08/2019

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by   Yuwen Li, et al.

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For a generalized Hodge--Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method controlling the error in the natural mixed variational norm. In particular, we obtain new quasi-optimal adaptive mixed methods for the scalar Poisson, vector Poisson, and Stokes equations. Comparing to existing adaptive mixed methods, the new methods control errors in both two variables.