We describe first measurement in a novel thin-layer channel flow cell designed for the investigation of heterogeneous electrocatalysis on porous catalysts. For the interpretation of the measurements, a macroscopic model for coupled species transport and reaction, which can be solved numerically, is feasible. In this paper, we focus on the limiting current. We compare numerical solutions of a macroscopic model to a generalization of a Leveque-type asymptotic estimate for circular electrodes, and to measurements obtained in the aforementioned flow cell. We establish that on properly aligned meshes, the numerical method reproduces the asymptotic estimate. Furthermore, we demonstrate that the measurements are partially performed in the sub-asymptotic regime, in which the boundary layer thickness exceeds the cell height. Using the inlet concentration and the diffusion coefficient from literature, we overestimate the limiting current. On the other hand, the use of fitted parameters leads to perfect agreement between model and experiment.

ABSTRACT. We introduce a time-implicite Voronoi box based finite volume discretization for the initial-boundary value problem of a scalar nonlinear viscous conservation law in a one, two-or threedimensional domain. Using notations from the theory of explicit finite volume methods for hyperbolic problems and results from the Perron-Frobenius theory of nonnegative matrices, we establish various existence, stability and uniqueness results for the discrete problem.The class of schemes introduced covers as well hyperbolic problems as well as nonlinear diffusion problems.To clarify our results, we provide numerical examples, and we show the practical relevance of our considerations with a groundwater flow example.

The paper is devoted to the inverse problem of identifying the coefficient in the main term of an elliptic differential equation describing the filtration of ground water. Experience suggests that the gradient of the piezometric head, i.e. Darcy's velocity, may have discontinuities and the transmissivity coefficient is a piecewise constant function.To solve this problem we use a modification of a direct method of Vainikko. Starting with a weak formulation of the problem, a suitable discretization is obtained by the method of least error. If necessary, this method can be combined with Tikhonov's regularization.The main difficulty consists of generating distributed state observations from measurements of the ground-water level. For this step we propose an optimized data preparation procedure using additional information such as knowledge of the sought parameter values at some points and lower and upper bounds for the parameter.Numerical tests confirm the expected local behaviour of the method, i.e. locally sufficiently many measurements provide locally satisfactory results. Two numerical examples, one with simulated data and the other with real life data, are given.

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