Year: 2014
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 745–761
Abstract
We analyze the convergence of a mixed finite element method for the elliptic Monge-Ampère equation in dimensions 2 and 3. The unknowns in the formulation, the scalar variable and a discrete Hessian, are approximated by Lagrange finite element spaces. The method originally proposed by Lakkis and Pryer can be viewed as the formal limit of a Hermann-Miyoshi mixed method proposed by Feng and Neilan in the context of the vanishing moment methodology. Error estimates are derived under the assumption that the continuous problem has a smooth solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-550
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 745–761
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Monge-Ampère mixed finite elements Lagrange elements fixed point.