A C1–C0 lowest-order virtual element method for the Stokes–Darcy interface problem in stream-function–pressure form is well-posed, optimally convergent, and mesh-flexible.
Polytopal Discontinuous Galerkin Discretizations of Coupled Non-Newtonian Stokes-Darcy Systems
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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.
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Stream function -- pressure virtual element methods for the Stokes--Darcy interface problem
A C1–C0 lowest-order virtual element method for the Stokes–Darcy interface problem in stream-function–pressure form is well-posed, optimally convergent, and mesh-flexible.