A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation

DOI10.1007/s00211-009-0283-xzbMath1201.65209OpenAlexW2145754040MaRDI QIDQ972581

Michael Neilan

Publication date: 21 May 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-009-0283-x

zbMATH Keywords

viscosity solutionlinearizationMonge-Ampère equationMorley element

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (15)

A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes ⋮ Finite element approximations of general fully nonlinear second order elliptic partial differential equations based on the vanishing moment method ⋮ Numerical analysis of strongly nonlinear PDEs ⋮ Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Ampère equation ⋮ New error estimates of the Morley element for the plate bending problems ⋮ An accelerated method for nonlinear elliptic PDE ⋮ A recovery-based linear \(C^0\) finite element method for a fourth-order singularly perturbed Monge-Ampère equation ⋮ A finite element/operator-splitting method for the numerical solution of the three dimensional Monge-Ampère equation ⋮ A Nonconforming Finite Element Approximation for the von Karman equations ⋮ A convexity enforcing \(C^0\) interior penalty method for the Monge-Ampère equation on convex polygonal domains ⋮ Spline element method for Monge-Ampère equations ⋮ 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation ⋮ Optimization approach for the Monge-Ampère equation ⋮ On the Numerical Solution of the Dirichlet Problem for the Elliptic $$(\sigma _2)$$ ( σ 2 ) Equation ⋮ Convergence of a fourth-order singular perturbation of then-dimensional radially symmetric Monge–Ampère equation

Cites Work

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• Time-delayed finite difference reaction-diffusion systems with nonquasimonotone functions
• Properties of the solutions of the linearized Monge-Ampere equation
• Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
• A Modified Characteristic Finite Element Method for a Fully Nonlinear Formulation of the Semigeostrophic Flow Equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• User’s guide to viscosity solutions of second order partial differential equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• Weak Existence for the Semigeostrophic Equations Formulated as a Coupled Monge--Ampère/Transport Problem
• Monge Ampère Equation: Applications to Geometry and Optimization
• The Mathematical Theory of Finite Element Methods
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