A locally conservative reduced flux reconstruction for elliptic problems
For researchers in model order reduction, this provides a way to enforce local conservation in reduced flux reconstructions, which is important for a posteriori error estimation and coupled flow problems.
This work presents a method to reconstruct a locally conservative flux from reduced solutions of parametric elliptic problems, enabling offline/online decomposition for error estimation and flow problems.
In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given reduced solution, that is locally conservative with respect to the underlying finite element grid. All components of the procedure depend separably on the parameter and allow for further use in offline/online decomposed computations, for instance in the context of a posterior error estimation or flow problems.