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Langmuir

Volumn 22, Issue 25, 2006, Pages 10666-10682

Adaptive finite element methods in electrochemistry

(3) Gavaghan, David J a Gillow, Kathryn a Süli, Endre a

a UNIVERSITY OF OXFORD (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CURRENT DENSITY; ELECTRIC CURRENTS; FINITE ELEMENT METHOD; INSULATING MATERIALS; MICROELECTRODES; PROBLEM SOLVING;

BOUNDARY SINGULARITY; EDGE EFFECTS; ELECTRODE EDGES;

ELECTROCHEMISTRY;

EID: 33845988040 PISSN: 07437463 EISSN: None Source Type: Journal
DOI: 10.1021/la061158l Document Type: Article

Times cited : (14)

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- The standard approach to error analysis that is widely reported in the electrochemical literature is to calculate a priori error bounds for finite difference methods. In general, this form of error analysis involves expanding the exact solution at a point as a Taylor series in powers of the mesh spacing on a regular mesh. Substitution of this expansion into the finite difference approximation provides a bound for the error in terms of powers of the mesh spacing and higher-order derivatives of the exact solution. For problems where the solution is smooth, this allows an approximation to the error in the problem to be obtained by repeatedly solving the problem on finer meshes, typically with the mesh spacing halved between successive meshes, which also allows the use of extrapolation methods such as Richardson extrapolation, A technical report exploring this approach has been provided by Østerby.49 The drawbacks of this approach are twofold. First, it does not give a
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