Hybridized numerical schemes for PDEs

Abstract: 

We describe hybridized finite element methods for partial differential equations, which are based on constructing local solutions on each triangle of a triangulation and patching these local solutions by flux continuity on intercell boundaries. The main advantages of this approach are that, firstly, it produces a locally conservative numerical scheme and, secondly, there is a large reduction in number of degree of freedom compared to conventional finite element methods.The talk includes hybridized numerical schemes for elliptic equations, stokes equations and elasticity problems.