A posteriori error estimators for hierarchical B-spline discretizations

In this paper, we develop a function-based a posteriori error estimators for the solution of linear second-order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré-type inequalities where the...