Adaptive finite element methods in electrochemistry.
In this article, we review some of our previous work that considers 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 su...
| Auteurs principaux: | , , |
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| Format: | Journal article |
| Langue: | English |
| Publié: |
2006
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| _version_ | 1826306652904620032 |
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| author | Gavaghan, D Gillow, K Süli, E |
| author_facet | Gavaghan, D Gillow, K Süli, E |
| author_sort | Gavaghan, D |
| collection | OXFORD |
| description | In this article, we review some of our previous work that considers 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 has involved 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, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique. |
| first_indexed | 2024-03-07T06:51:13Z |
| format | Journal article |
| id | oxford-uuid:fc9f1570-c8fd-472f-ba67-1dc05270d918 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:51:13Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:fc9f1570-c8fd-472f-ba67-1dc05270d9182022-03-27T13:22:14ZAdaptive finite element methods in electrochemistry.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fc9f1570-c8fd-472f-ba67-1dc05270d918EnglishSymplectic Elements at Oxford2006Gavaghan, DGillow, KSüli, EIn this article, we review some of our previous work that considers 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 has involved 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, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique. |
| spellingShingle | Gavaghan, D Gillow, K Süli, E Adaptive finite element methods in electrochemistry. |
| title | Adaptive finite element methods in electrochemistry. |
| title_full | Adaptive finite element methods in electrochemistry. |
| title_fullStr | Adaptive finite element methods in electrochemistry. |
| title_full_unstemmed | Adaptive finite element methods in electrochemistry. |
| title_short | Adaptive finite element methods in electrochemistry. |
| title_sort | adaptive finite element methods in electrochemistry |
| work_keys_str_mv | AT gavaghand adaptivefiniteelementmethodsinelectrochemistry AT gillowk adaptivefiniteelementmethodsinelectrochemistry AT sulie adaptivefiniteelementmethodsinelectrochemistry |