Mixed finite element method

Summary

A mixed finite element method approximates two or more unknown fields of a boundary value problem at once, each in its own finite element space. It starts from a saddle-point formulation, such as velocity and pressure for Stokes flow, or flux and potential for the Poisson equation. The spaces cannot be chosen independently: stability requires the Ladyzhenskaya–Babuška–Brezzi condition. Mixed methods give accurate fluxes that satisfy conservation element by element, which matters for flow in porous media. See the definition.