The double adaptivity paradigm

We present an efficient implementation of the double adaptivity algorithm Cohen et al. (2012) within setting Petrov–Galerkin method with optimal test functions. apply this to ultraweak variational formulation a general linear problem discretized standard Galerkin finite element method. As example, we demonstrate feasibility in context convection-dominated diffusion problem. The presented ideas, however, virtually any well-posed system first-order partial differential equations, including singular perturbation problems.