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

2024/02/26 by Luigi C. Berselli, Berselli, Luigi C., Alex Kaltenbach +1 · 1 citation
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2402.16606

Abstract

In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady p(⋅,⋅)-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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