A static condensation reduced basis element method: approximation and {a posteriori} error estimation (Q2836462)

The reduced basis element (RBE) method computes finite element solutions of partial differential equations using domain decomposition and parametric order reduction. The authors' approach uses static condensation at the interdomain level, a conforming eigenfunction representation at the interface level, and reduced basis (RB) approximation of finite element bubble functions at the intradomain level. Components are completely interchangeable and interoperable and the analysis is bottom-up, from a library of components to many possible systems, contrasting with the classical top-down approach. The authors' approach allows a posteriori error bounds to be calculated using only interface degrees of freedom and intradomain quantities, and provides flexibility in the inexpensive online stage.