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arXiv · 2606.28914

Pressure-robust ALE space-time DG method for the Stokes equations on moving domains

L. Beirão da Veiga·S. Gómez·K. B. Haile
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Abstract

We propose and analyze a space-time discontinuous Galerkin method for the incompressible Stokes equations on moving domains within the arbitrary Lagrangian-Eulerian setting. We use a contravariant Piola map in the definition of the discrete velocity space to preserve the pointwise divergence-free property on the discrete level. We show that the method is inf-sup stable, with no constraints on the spatial mesh or the time partition. We also establish a priori error estimates in the energy norm for arbitrary degrees of approximation in space and time. For piecewise-constant and piecewise-linear approximations in time, we show that the method is also robust at low viscosity regimes, and provide numerical evidence suggesting that this property extends to high-order cases as well. We present several numerical experiments to validate our theoretical findings.

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L. Beirão da Veiga, S. Gómez, K. B. Haile. 2026-06-27. Pressure-robust ALE space-time DG method for the Stokes equations on moving domains. https://arxiv.org/abs/2606.28914

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