  We present an $n$-dimensional marked bisection method for unstructured
conformal meshes. We devise the method for local refinement in adaptive
$n$-dimensional applications. To this end, we propose a mesh marking
pre-process and three marked bisection stages. The pre-process marks the
initial mesh conformingly. Then, in the first $n-1$ bisections, the method
accumulates in reverse order a list of new vertices. In the second stage, the
$n$-th bisection, the method uses the reversed list to cast the bisected
simplices as reflected simplices, a simplex type suitable for newest vertex
bisection. In the final stage, beyond the $n$-th bisection, the method switches
to newest vertex bisection. To allow this switch, after the second stage, we
check that under uniform bisection the mesh simplices are conformal and
reflected. These conditions are sufficient to use newest vertex bisection, a
bisection scheme guaranteeing key advantages for local refinement. Finally, the
results show that the proposed bisection is well-suited for local refinement of
unstructured conformal meshes.
