Finite element approximations of the three dimensional Monge-Ampère equation
نویسندگان
چکیده
منابع مشابه
Finite Element Approximations of the Three Dimensional Monge-ampère Equation
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the wellposedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experim...
متن کاملA nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation
In this paper, we study finite element approximations of the viscosity solution of the fully nonlinear Monge-Ampère equation, det(Du) = f (> 0) using the well-known nonconforming Morley element. Our approach is based on the vanishing moment method, which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and Feng in [15]. The vanishin...
متن کاملContinuity Estimates for the Monge-Ampère Equation
In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semi-geostrophic equation arising in meteorology.
متن کاملQuadratic Mixed Finite Element Approximations of the Monge-ampère Equation in 2d
We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampère equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar variable and the Hessian matrix.
متن کاملMixed Finite Element Methods for the Fully Nonlinear Monge-Ampère Equation Based on the Vanishing Moment Method
This paper studies mixed finite element approximations of the viscosity solution to the Dirichlet problem for the fully nonlinear Monge–Ampère equation det(D2u0) = f (> 0) based on the vanishing moment method which was proposed recently by the authors in [X. Feng and M. Neilan, J. Scient. Comp., DOI 10.1007/s10915-008-9221-9, 2008]. In this approach, the second-order fully nonlinear Monge–Ampèr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2012
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2011067