Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation

Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation

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.