A new MOX Report entitled “A nonconforming method for a generalized Darcy-Forchheimer model” by Botti, M.; Mascotto, L.; Mosconi, M. has appeared in the MOX Report Collection.
Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/36-2026.pdf
Abstract: We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed in [V. Girault and M. F. Wheeler. Numerical discretization of a Darcy-Forchheimer model. Numer. Math. 2008], we consider general, i.e., non-quadratic, 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.
