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arXiv · 2012.01898

Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems

Paola F. Antonietti·Lorenzo Mascotto·Marco Verani·Stefano Zonca
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Abstract

We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a fluid-structure interaction problem and we numerically explore the stability properties of the method.

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Paola F. Antonietti, Lorenzo Mascotto, Marco Verani, Stefano Zonca. 2020-12-03. Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems. https://arxiv.org/abs/2012.01898

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