Journal of Scientific Computing· 2026Q1
Pressure-Robust Staggered DG Methods for the Navier–Stokes Equations on General Meshes
- 2citations
- Q1SCImago
- 2026year
Short summary
New staggered discontinuous Galerkin (DG) methods for Navier-Stokes equations ensure velocity accuracy is independent of pressure and Reynolds number for small rotational forces.
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Key points
- Designed and analyzed staggered discontinuous Galerkin (DG) methods for stationary Navier-Stokes equations on polygonal meshes.
- Achieved exact divergence-free velocity and pressure-robustness, where velocity approximation is independent of pressure.
- Proposed an edge-wise stabilization for the nonlinear convective term that preserves non-negativity.
- Proved optimal L2 convergence estimates for all variables.
- Demonstrated velocity error independence from Reynolds number and pressure for small rotational forces, with potential for superconvergence.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In this paper, we design and analyze staggered discontinuous Galerkin methods of arbitrary polynomial orders for the stationary Navier–Stokes equations on polygonal meshes. The exact divergence-free condition for the velocity is satisfied thanks to the carefully designed finite element spaces. The resulting method is pressure-robust so that the pressure approximation does not influence the velocity approximation, which is highly appreciated from a practical point of view. An edge-wise stabilization is proposed for the nonlinear convective term, which preserves the non-negativity. The optimal convergence estimates for all the variables in the $$L^2$$ L 2 norm are proved. For a small enough rotational force, the velocity error is independent of the Reynolds number and of the pressure. Superconvergence can be achieved for the velocity error under a suitable projection. Numerical experiments are provided to validate the theoretical findings and demonstrate the performance of the proposed method.
The authors' abstract, as published at the source. Journal of Scientific Computing, 2026 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering