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Volume 11, Issue 4
Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation

G. Awanou & H. Li

Int. J. Numer. Anal. Mod., 11 (2014), pp. 745-761.

Published online: 2014-11

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  • 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.

  • Keywords

Monge-Ampère, mixed finite elements, Lagrange elements, fixed point.

  • AMS Subject Headings

65N30, 35J25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-745, author = {G. Awanou and H. Li}, title = {Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/550.html} }
TY - JOUR T1 - Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation AU - G. Awanou & H. Li JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 745 EP - 761 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/550.html KW - Monge-Ampère, mixed finite elements, Lagrange elements, fixed point. AB -

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.

G. Awanou and H. Li. (2014). Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation. International Journal of Numerical Analysis and Modeling. 11 (4). 745-761. doi:
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