SIMULATION IN ELECTROCHEMISTRY USING THE FINITE ELEMENT METHOD. PART 1. THE ALGORITHM

Abstract The finite element method (FEM) is well known in engineering technology. Numerous commercial packages are available. Extensions using an algorithm with an adaptive grid make this method very useful for a great variety of problems. This paper shows the applicability of this powerful tool to electrochemical problems in a general manner. In a first step, the mathematical equations are generalised to handle flexibly different electrochemical mechanisms and electrode geometries. Then, the finite element method is applied to these formulations and electrochemical boundary conditions are introduced. The spatial and time discretisations are discussed and a new method for flux calculation is introduced. Essential advantages of the adaptive finite element (AFE) algorithm are its flexibility and its applicability to many types of electrochemical processes and methods.

[1]  Nicholas Stevens,et al.  Finite Element Simulations in Electrochemistry. 2. Hydrodynamic Voltammetry , 1997 .

[2]  Nicholas Stevens,et al.  Computer-aided design and experimental application of a novel electrochemical cell: The confluence reactor , 1998 .

[3]  Jürgen Heinze,et al.  Digital simulation of cyclic voltammetric curves by the implicit Crank-Nicolson technique , 1984 .

[4]  Jürgen Heinze,et al.  Cyclovoltammetrie — die „Spektroskopie”︁ des Elektrochemikers , 1984 .

[5]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[6]  A. Ševčík,et al.  Oscillographic polarography with periodical triangular voltage , 1948 .

[7]  David K. Gosser,et al.  Cyclic Voltammetry: Simulation and Analysis of Reaction Mechanisms , 1993 .

[8]  Hubert H. Girault,et al.  Finite Element Simulation of the Amperometric Response of Recessed and Protruding Microband Electrodes in Flow Channels , 1997 .

[9]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[10]  R. S. Nicholson,et al.  Theory of Stationary Electrode Polarography. Single Scan and Cyclic Methods Applied to Reversible, Irreversible, and Kinetic Systems. , 1964 .

[11]  Hubert H. Girault,et al.  Coplanar interdigitated band electrodes for electrosynthesis. Part 5: finite element simulation of paired reactions , 1998 .

[12]  Zbigniew Stojek,et al.  The finite element method for solutions of electroanalytical problems: Part II. Hermite approximation with variable space grid , 1984 .

[13]  A. Bard,et al.  Scanning electrochemical microscopy. Theory of the feedback mode , 1989 .

[14]  Hubert H. Girault,et al.  Finite element simulation of the chronoamperometric response of recessed and protruding microdisc electrodes , 1997 .

[15]  Jürgen Heinze,et al.  Cyclic Voltammetry—“Electrochemical Spectroscopy”. New Analytical Methods (25) , 1984 .

[16]  F. Nicolas,et al.  Modelling coupled transfers in an industrial fluorine electrolyser , 1998 .

[17]  Manfred Rudolph,et al.  A fast implicit finite difference algorithm for the digital simulation of electrochemical processes , 1991 .

[18]  W. Hackbusch.  Iterative Lösung großer schwachbesetzter Gleichungssysteme , 1991 .

[19]  Manfred Rudolph,et al.  Digital simulations with the fast implicit finite difference (FIFD) algorithm: Part II. An improved treatment of electrochemical mechanisms with second-order reactions , 1992 .

[20]  Zbigniew Stojek,et al.  The finite element method for solution of electroanalytical problems , 1984 .

[21]  J. Randles,et al.  A cathode ray polarograph. Part II.—The current-voltage curves , 1948 .