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Nonconforming finite-element discretization of convex variational problems
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Ortner, Christoph. (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Vol.31 (No.3). pp. 847-864. ISSN 0272-4979
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Official URL: http://dx.doi.org/10.1093/imanum/drq004
Abstract
The Lavrentiev gap phenomenon is a well-known effect in the calculus of variations, related to singularities of minimizers. In its presence, conforming finite-element methods are incapable of reaching the energy minimum. By contrast, it is shown in this work that for convex variational problems the nonconforming Crouzeix–Raviart finite-element discretization always converges to the correct minimizer and that the discrete energy converges to the correct limit.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | IMA Journal of Numerical Analysis |
| Publisher: | Oxford University Press |
| ISSN: | 0272-4979 |
| Date: | 3 July 2011 |
| Volume: | Vol.31 |
| Number: | No.3 |
| Page Range: | pp. 847-864 |
| Identification Number: | 10.1093/imanum/drq004 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43773 |
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