Finite element approximations of the three dimensional Monge-Ampère equation
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN: 2804-7214, Vol: 46, Issue: 5, Page: 979-1001
2012
- 38Citations
- 74Usage
- 6Captures
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Metrics Details
- Citations38
- Citation Indexes38
- 38
- CrossRef22
- Usage74
- Downloads69
- Abstract Views5
- Captures6
- Readers6
Article Description
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings. © EDP Sciences, SMAI, 2012.
Bibliographic Details
https://repository.lsu.edu/mathematics_pubs/147; https://digitalcommons.lsu.edu/mathematics_pubs/147
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84861913468&origin=inward; http://dx.doi.org/10.1051/m2an/2011067; http://www.esaim-m2an.org/10.1051/m2an/2011067; http://www.esaim-m2an.org/10.1051/m2an/2011067/pdf; https://repository.lsu.edu/mathematics_pubs/147; https://repository.lsu.edu/cgi/viewcontent.cgi?article=1146&context=mathematics_pubs; https://digitalcommons.lsu.edu/mathematics_pubs/147; https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=1146&context=mathematics_pubs; https://dx.doi.org/10.1051/m2an/2011067; https://www.esaim-m2an.org/articles/m2an/abs/2012/05/m2an110067/m2an110067.html
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