# A locally conservative reduced flux reconstruction for elliptic problems

## TL;DR

This paper introduces a new flux reconstruction method for parametric elliptic problems that ensures local conservation and is suitable for efficient offline/online computations in reduced order modeling.

## Contribution

The paper presents a novel, parameter-separable flux reconstruction technique that guarantees local conservation in reduced order models of elliptic problems.

## Key findings

- Ensures local conservation of flux in reduced models.
- Compatible with offline/online computational frameworks.
- Applicable to flow problems and error estimation.

## Abstract

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.