Polytopal Discontinuous Galerkin Discretizations of Coupled Non-Newtonian Stokes-Darcy Systems

Keywords

Code:
45/2026
Title:
Polytopal Discontinuous Galerkin Discretizations of Coupled Non-Newtonian Stokes-Darcy Systems
Date:
Wednesday 10th June 2026
Author(s):
Antonietti, P.F.; Botti, M.; Parolini, N.; Pederzoli, V.; Verani, M.
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Abstract:
We propose and analyze a polytopal discontinuous Galerkin method for the numerical approximation of a coupled non-Newtonian Stokes-Darcy system modeling the interaction between a non-Newtonian free-flow fluid and a non-Newtonian flow through a porous medium. Due to its geometric flexibility and arbitrary-order accuracy, the proposed discretization scheme is well-suited to configurations with complex geometries. We provide a complete a-priori analysis that considers shear-dependent and velocity-dependent non-Newtonian viscosity models for the free-flow and porous media regions, respectively. The well-posedness, stability, and error bounds of the method are established in the framework of generalized inf-sup theory. Error estimates are confirmed by numerical results.