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

Yuwen Li

Published 2019-07-08Version 1

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.