Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors
Numerical Analysis
2021-03-02 v2 Numerical Analysis
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.
Cite
@article{arxiv.1907.03852,
title = {Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors},
author = {Yuwen Li},
journal= {arXiv preprint arXiv:1907.03852},
year = {2021}
}
Comments
29 pages