  Mixed finite element methods with flux errors in $H(div)$-norms and
div-least-squares finite element methods require a separate marking strategy in
obligatory adaptive mesh-refining. The refinement indicator $\sigma^2(\mathcal
T,K)=\eta^2(\mathcal T,K)+\mu^2(K)$ of a finite element domain $K$ in an
admissible triangulation $\mathcal T$ consists of some residual-based error
estimator $\eta(\mathcal T,K)$ with some reduction property under local
mesh-refining and some data approximation error $\mu(K)$. Separate marking
means either D\"orfler marking if $\mu^2(\mathcal T) \leq \kappa
\eta^2(\mathcal T)$ or otherwise an optimal data approximation algorithm runs
with controlled accuracy as established in [Carstensen, Rabus, Math.Comp. 2011;
Rabus, J.Numer.Math. 2015].
  The axioms are abstract and sufficient conditions on the estimators
$\eta(\mathcal T,K)$ and data approximation errors $\mu(K)$ for optimal
asymptotic convergence rates. The enfolded set of axioms simplifies
\cite{CFP14} for collective marking, treats separate marking established for
the first time in an abstract framework, generalizes [Carstensen, Park, SIAM
J.Numer.Anal. 2015] for least-squares schemes, and extends [Carstensen, Rabus,
Math.Comp. 2011] to the mixed FEM with flux error control in $H(div)$.

Numerical Analysis