A nonconforming method for a generalized Darcy-Forchheimer model

Keywords

Advanced Numerical Methods for Scientific Computing
Geosciences/Protection of Land and Water Resources
Code:
36/2026
Title:
A nonconforming method for a generalized Darcy-Forchheimer model
Date:
Tuesday 5th May 2026
Author(s):
Botti, M.; Mascotto, L.; Mosconi, M.
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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.