From face to element unknowns by local static condensation with application to nonconforming finite elements

► We derive a new local static condensation strategy for nonconforming finite elements. ► It allows to reduce the number of unknowns, from one per face to one per element. ► The resulting matrices are sparse, generally positive definite but nonsymmetric. ► Their condition number is quite insensitive to anisotropies and inhomogeneties. ► Application to (non) linear (un) steady problems shows important computational savings. ► A general abstract framework is provided and analysed.