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arXiv · 2611.08429

Preconditioning for the time-dependent Stokes equations: stage-weighted Radau IIA and weighted discontinuous Galerkin time-stepping

Esteban Henríquez·Jeonghun J. Lee·Sander Rhebergen
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Abstract

We determine field-of-values equivalent preconditioners for the time-dependent Stokes equations discretized in time by stage-weighted Radau IIA Runge--Kutta time-stepping and discontinuous Galerkin time-stepping methods. By weighing each stage of the Radau IIA Runge--Kutta method differently we obtain preconditioners that are field-of-values equivalent, with constants independent of viscosity, timestep, and mesh size, to the system matrix. Similarly, by using weighted inner products in time to define the discontinuous Galerkin time-stepping method, we again obtain field-of-values equivalent preconditioners for the resulting system matrix. Numerical experiments are performed in two and three-dimensions which demonstrate robustness of the proposed preconditioners.

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Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen. 2026-11-05. Preconditioning for the time-dependent Stokes equations: stage-weighted Radau IIA and weighted discontinuous Galerkin time-stepping. https://arxiv.org/abs/2611.08429

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