Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-optimal adaptive mixed finite element methods for controlling
  natural norm errors   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.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th