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arXiv · 2506.11566

Refined stability estimates for mixed problems by exploiting semi norm arguments

Nicolas Gauger·Alexander Linke·Christian Merdon
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Abstract

Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible Navier--Stokes equations. In fact, kernels of these semi norms are shown to be connected to physical regimes in applications and are related to some well-known consistency errors in classical discretizations of mixed problems. Consequently, significantly sharper stability estimates for solutions close to these physical regimes are obtained.

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Nicolas Gauger, Alexander Linke, Christian Merdon. 2025-06-13. Refined stability estimates for mixed problems by exploiting semi norm arguments. https://arxiv.org/abs/2506.11566

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