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

2020/09/02 by Yuwen Li · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.1090/mcom/3590

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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• Smoother-type a posteriori error estimates for finite element methods

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