A nonconforming method for a generalized Darcy-Forchheimer model

Abstract

We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed by Girault and Wheeler, we consider general, i.e., nonquadratic, Forchheimer nonlinearities; we admit mixed, inhomogeneous boundary conditions; we allow for more general, i.e., with lower Lebesgue regularity, permeability tensors; we construct general-order schemes; we prove convergence to the exact solution under low regularity assumptions, based on novel Sobolev-trace inequalities for broken spaces; we derive error estimates of general-order assuming extra regularity of the exact solution and data; we present numerical results assessing the performance of the proposed schemes for different types of nonlinearity and nonlinear solvers.