Adaptative finite element simulation of currents at microelectrodes to a guaranteed accuracy. Application to a simple model problem |
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| Affiliation: | 1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK;2. Nuffield Department of Anaesthetics, Radcliffe Infirmary, Oxford OX2 6HE, UK;3. Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, UK;1. IITB-Monash Research Academy, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;2. Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai 400076, India;3. Talga Technologies Ltd, 184 The Bradley Centre, Cambridge Science park, Milton Road, Cambridge CB4 0GA, UK;4. Department of Materials Science and Engineering, Monash University, Wellington Road, Clayton, VIC 3800, Australia;1. Department of Chemical Engineering, Laboratory of Advanced Materials (MOE), Tsinghua University, Beijing 100084, PR China;2. State Key Laboratory of Precision Measurement Technology and Instrument, Department of Precision Instrument, Tsinghua University, Beijing 100084, PR China;3. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, PR China;1. Centre for Nanoscience and Technology, Department of Mechanical Engineering, Mepco Schlenk Engineering College, Sivakasi 626 005, Tamil Nadu, India;2. Faculty of Allied Health Sciences, Chettinad Hospital and Research Institute, Chettinad Academy of Research and Education (CARE), Kelambakkam, Chennai 603103, India;3. Department of Electronics and Communications Engineering, National Institute of Technology, Puducherry, Karaikal 609609, India;1. Department of Chemical and Biological Engineering, Iowa State University, United States;2. The Solae Company, 4272 S Mendenhall Rd., Memphis, TN 38141, United States;3. Laboratoire de Chimie Agro-industrielle (LCA), Université de Toulouse, INRA, INPT, Toulouse, France |
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| Abstract: | In this series of papers we consider the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the ‘edge-effect’. Our approach to overcoming this problem involves the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm. This allows us to calculate the current to within a prescribed tolerance. We begin by demonstrating the power of the method for a simple model problem — an E reaction mechanism at a microdisc electrode — for which the analytical solution is known. In this paper we give the background to the problem, and show how an a posteriori error bound can be used to drive an adaptive mesh-generation algorithm. We then use the algorithm to solve our model problem and obtain very accurate results on comparatively coarse meshes in minimal computing time. We give the technical details of the background theory and the derivation of the error bound in the accompanying paper. |
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