A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem
<|reference_start|>A polytopal discontinuous Galerkin method for the pseudo-stress formulation of the unsteady Stokes problem: 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.<|reference_end|>
@article{antonietti2024a,
    title={A polytopal discontinuous Galerkin method for the pseudo-stress
  formulation of the unsteady Stokes problem},
    author={Paola F. Antonietti, Michele Botti, Alessandra Cancrini, Ilario
  Mazzieri},
    journal={arXiv preprint arXiv:2408.08760},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08760},
    primaryClass={math.NA cs.NA}
}