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Adaptive finite element methods in electrochemistry.

David J Gavaghan1, Kathryn Gillow, Endre Süli

  • 1Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.

Langmuir : the ACS Journal of Surfaces and Colloids
|November 30, 2006
PubMed
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This study presents an adaptive finite element method for accurately simulating currents at microelectrodes. The approach effectively handles the boundary singularity, or edge effect, crucial for precise microelectrode simulations.

Area of Science:

  • Electrochemistry
  • Computational Science

Background:

  • Microelectrodes are essential in various scientific applications.
  • Numerical simulation of microelectrodes is challenging due to boundary singularities (edge effects).

Purpose of the Study:

  • To present a robust numerical method for simulating currents at microelectrodes.
  • To address the challenge of boundary singularities in microelectrode simulations.

Main Methods:

  • Adaptive finite element approach.
  • Derivation of an a posteriori error bound for current approximation.
  • Mesh generation driven by error bounds.

Main Results:

  • Successfully simulated currents at microelectrodes with high accuracy.

Related Experiment Videos

  • Effectively managed the boundary singularity (edge effect).
  • Demonstrated applicability across various steady-state scenarios.

    • Conclusions:

    • The adaptive finite element method provides accurate microelectrode current simulations.
    • The error-bound-driven adaptive meshing overcomes edge effect challenges.
    • The technique is broadly applicable to steady-state microelectrode problems.