A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem

Keywords

Advanced Numerical Methods for Scientific Computing
Geosciences/Protection of Land and Water Resources
Code:
54/2024
Title:
A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem
Date:
Wednesday 14th August 2024
Author(s):
Antonietti, P.F.; Botti, M.; Cancrini, A.; Mazzieri, I.
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Abstract:
This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest in non-Newtonian flows and coupled interface problems, where stress assumes a fundamental role. The space-time discretization of the problem is achieved by combining the PolydG approach with the implicit theta-method time integration scheme. For both the semi- and fully-discrete problems we present a detailed stability analysis. Moreover, we derive convergence estimates for the fully discrete space-time discretization. A set of verification tests is presented to verify the theoretical estimates and the application of the method to cases of engineering interest.
This report, or a modified version of it, has been also submitted to, or published on
SIAM Journal on Scientific Computing