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 - <p style="text-align: justify;">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.</p>