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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{henriquez2026preconditioning,
  title = {{Preconditioning for the time-dependent Stokes equations: stage-weighted Radau IIA and weighted discontinuous Galerkin time-stepping}},
  author = {Esteban Henríquez and Jeonghun J. Lee and Sander Rhebergen},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08429},
  eprint = {2611.08429},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08429},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Preconditioning for the time-dependent Stokes equations: stage-weighted Radau IIA and weighted discontinuous Galerkin time-stepping
AU  - Esteban Henríquez
AU  - Jeonghun J. Lee
AU  - Sander Rhebergen
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08429
UR  - https://arxiv.org/abs/2611.08429
AB  - 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.
ER  -