The double adaptivity paradigm
(How to circumvent the discrete inf-sup conditions of Babuška and Brezzi)
Leszek Demkowicz, Thomas Führer, Norbert Heuer, and Xiaochuan Tian
Comput. Math. Appl. 95, 41–66, 2021.
We present an efficient implementation of the double adaptivity algorithm of Cohen, Dahmen and
Welpert within the setting of the Petrov–Galerkin Method with optimal test functions, for both classical
and the ultraweak variational formulations, and a standard Galerkin finite element (FE) technology.
We use a 1D convection-dominated diffusion problem as an example but the presented ideas apply to
virtually any well-posed system of first order PDEs including singular perturbation problems.