Probing the Numerical Convergence of a Commercial Finite Element Software in Electrochemical Simulations

We studied the efficiency and accuracy of a general purpose finite element software in the numerical solution of electrochemical models. Typical numerical complications like boundary singularities, stiffness and multiscale problems were addressed. The convergence order was determined for various mes...

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Bibliographic Details
Published in:Denki kagaku oyobi kōgyō butsuri kagaku 2014/11/05, Vol.82(11), pp.966-973
Main Authors: CARNEIRO-NETO, Evaldo Batista, SIKORA, Mariana Souza, PEREIRA, Ernesto Chaves, LOPES, Mauro Chierici
Format: Article
Language:English
Subjects:
Accuracy
Adjustment
Boundary Singularities
Computational Electrochemistry
Computer programs
Convergence
Finite element method
Mathematical analysis
Mathematical models
Multi-Scale Modelling
Software
Stiff Problems
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Summary:We studied the efficiency and accuracy of a general purpose finite element software in the numerical solution of electrochemical models. Typical numerical complications like boundary singularities, stiffness and multiscale problems were addressed. The convergence order was determined for various mesh refinement strategies. As a general rule, the numerical efficiency of the software proved adequate to the problems dealt, but the default generated meshes and the adaptive mesh adjustment do not work properly, if high levels of accuracy are required. Therefore, a manual adjustment of the mesh control parameters is indispensable. A thorough discussion of the problem of adjusting the mesh was presented to serve as a general introduction to the subject for beginners in the field. Additionally, it was suggested a general approach for mesh optimization through which the convergence rate can be considerably increased.
ISSN:1344-3542
2186-2451
DOI:10.5796/electrochemistry.82.966