Analysis of Galerkin Methods for the Fully Nonlinear Monge-Ampère Equation
نویسندگان
چکیده
منابع مشابه
Analysis of Galerkin Methods for the Fully Nonlinear Monge-Ampère Equation
This paper develops and analyzes finite element Galerkin and spectral Galerkin methods for approximating viscosity solutions of the fully nonlinear Monge-Ampère equation det(D2u0) = f (> 0) based on the vanishing moment method which was developed by the authors in [17, 15]. In this approach, the Monge-Ampère equation is approximated by the fourth order quasilinear equation −ε∆2uε + det D2uε = f...
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In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well a...
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In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well a...
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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...
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ژورنال
عنوان ژورنال: Journal of Scientific Computing
سال: 2010
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-010-9439-1