Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations

Luigi C. Berselli; Alex Kaltenbach

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arXiv · 2402.16606

Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations

Luigi C. Berselli·Alex Kaltenbach

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Abstract

In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation in space. Moreover, numerical experiments are carried out that supplement the theoretical findings.

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Luigi C. Berselli, Alex Kaltenbach. 2024-02-26. Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations. https://arxiv.org/abs/2402.16606

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