Assess Dörfler marking on irreparably distorted meshes

Determine whether Dörfler marking retains good practical behavior when adaptive finite element refinement begins from a distorted mesh that cannot be improved.

Background

The paper notes that convergence and optimality theory for adaptive finite element methods generally assumes shape-regular meshes. Its numerical study instead focuses on fixed coarse or distorted meshes and certified a posteriori estimation.

An unresolved issue is whether the standard Dörfler marking strategy remains effective in practice when the initial mesh is distorted and mesh improvement is unavailable or prohibited. This question concerns adaptivity rather than the reliability of the equilibrated flux estimator itself.