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A Priori Error Rates for Fully-Discrete Finite Elements of the Unsteady p(.,.)-Stokes Equations

How to prove convergence rates for a numerical scheme that solves a non-Newtonian incompressible flow whose power-law exponent varies in space and time: discretize with backward Euler in time and inf-sup-stable finite elements in space, then bound the velocity error under fractional regularity of the velocity and pressure. Students learn why a variable exponent complicates the analysis and how numerical experiments confirm the rates are optimal for exponents at least two.

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Error analysis for a fully-discrete finite element approximation of the unsteady p(·, ·)-Stokes

A numerical-analysis paper deriving a priori error estimates for a fully-discrete finite element scheme solving the unsteady p(.,.)-Stokes equations, a model of incompressible non-Newtonian (smart / …