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    Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Fuhrmann, Jürgen; Linke, Alexander; Merdon, Christian; Neumann, Felix; Streckenbach, Timo; Baltruschat, Helmut; Khodayari, Mehdi
    Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with the physical bounds namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocities from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using known real-istic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the scope of the presented numerical tools.
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    Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Linke, Alexander; Merdon, Christian; Neilan, Michael; Neumann, Felix
    Nearly all classical inf-sup stable mixed finite element methods for the incompressible Stokes equations are not pressure-robust, i.e., the velocity error is dependent on the pressure. However, recent results show that pressure-robustness can be recovered by a non-standard discretization of the right hand side alone. This variational crime introduces a consistency error in the method which can be estimated in a straightforward manner provided that the exact velocity solution is sufficiently smooth. The purpose of this paper is to analyze the pressurerobust scheme with low regularity. The numerical analysis applies divergence-free H1-conforming Stokes finite element methods as a theoretical tool. As an example, pressure-robust velocity and pressure a-priori error estimates will be presented for the (first order) nonconforming CrouzeixRaviart element. A key feature in the analysis is the dependence of the errors on the Helmholtz projector of the right hand side data, and not on the entire data term. Numerical examples illustrate the theoretical results.