TY - JOUR
T1 - Error Analysis of a Mixed Finite Element Method for the Monge-Ampère Equation
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 - <p style="text-align: justify;">We analyze the convergence of a mixed finite element method for the elliptic Monge-Ampère &nbsp;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.</p>