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Volume 19, Issue 5
Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation

Jamal Adetola, Bernadin Ahounou, Gerard Awanou & Hailong Guo

Int. J. Numer. Anal. Mod., 19 (2022), pp. 669-684.

Published online: 2022-08

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  • Abstract

In this paper, we are interested in the analysis of the convergence of a low order mixed finite element method for the Monge-Ampère equation. The unknowns in the formulation are the scalar variable and the discrete Hessian. The distinguished feature of the method is that the unknowns are discretized using only piecewise linear functions. A superconvergent gradient recovery technique is first applied to the scalar variable, then a piecewise gradient is taken, the projection of which gives the discrete Hessian matrix. For the analysis we make a discrete elliptic regularity assumption, supported by numerical experiments, for the discretization based on gradient recovery of an equation in non divergence form. A numerical example which confirms the theoretical results is presented.

  • Keywords

Monge-Ampère, mixed finite element, gradient recovery, non divergence form.

  • AMS Subject Headings

65N30, 65N15, 35J96

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hailong.guo@unimelb.edu.au (Hailong Guo)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-19-669, author = {Adetola , JamalAhounou , BernadinAwanou , Gerard and Guo , Hailong}, title = {Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {5}, pages = {669--684}, abstract = {

In this paper, we are interested in the analysis of the convergence of a low order mixed finite element method for the Monge-Ampère equation. The unknowns in the formulation are the scalar variable and the discrete Hessian. The distinguished feature of the method is that the unknowns are discretized using only piecewise linear functions. A superconvergent gradient recovery technique is first applied to the scalar variable, then a piecewise gradient is taken, the projection of which gives the discrete Hessian matrix. For the analysis we make a discrete elliptic regularity assumption, supported by numerical experiments, for the discretization based on gradient recovery of an equation in non divergence form. A numerical example which confirms the theoretical results is presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20934.html} }
TY - JOUR T1 - Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation AU - Adetola , Jamal AU - Ahounou , Bernadin AU - Awanou , Gerard AU - Guo , Hailong JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 669 EP - 684 PY - 2022 DA - 2022/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20934.html KW - Monge-Ampère, mixed finite element, gradient recovery, non divergence form. AB -

In this paper, we are interested in the analysis of the convergence of a low order mixed finite element method for the Monge-Ampère equation. The unknowns in the formulation are the scalar variable and the discrete Hessian. The distinguished feature of the method is that the unknowns are discretized using only piecewise linear functions. A superconvergent gradient recovery technique is first applied to the scalar variable, then a piecewise gradient is taken, the projection of which gives the discrete Hessian matrix. For the analysis we make a discrete elliptic regularity assumption, supported by numerical experiments, for the discretization based on gradient recovery of an equation in non divergence form. A numerical example which confirms the theoretical results is presented.

Adetola , JamalAhounou , BernadinAwanou , Gerard and Guo , Hailong. (2022). Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation. International Journal of Numerical Analysis and Modeling. 19 (5). 669-684. doi:
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