Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation

Low Order Mixed Finite Element Approximations of the Monge-Ampère Equation

Year:    2022

Author:    Jamal Adetola, Bernadin Ahounou, Gerard Awanou, Hailong Guo

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 5 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2022-IJNAM-20934

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 5 : pp. 669–684

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

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

Author Details

Jamal Adetola

Bernadin Ahounou

Gerard Awanou

Hailong Guo