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

Li, Yuwen

doi:10.1090/mcom/3590

Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors
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by Yuwen Li;

Math. Comp. 90 (2021), 565-593

DOI: https://doi.org/10.1090/mcom/3590

Published electronically: November 23, 2020

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Abstract:

For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic forms is trivial. In particular, we obtain new quasi-optimal adaptive mixed methods for the Hodge Laplace, Poisson, and Stokes equations. Comparing to existing adaptive mixed methods, the new methods control errors in both variables.

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