A family of nonconforming elements for the Brinkman problem

We propose and analyse a new family of nonconforming elements for the Brinkman problem of porous media flow. The corresponding finite element methods are robust with respect to the limiting case of Darcy flow, and the discretely divergence-free functions are in fact divergence-free. Therefore, in the absence of sources and sinks, the method is strongly mass-conservative. We also show how the proposed elements are part of a discrete de Rham complex.