Finite element methods for fully nonlinear second order PDEs based on a discrete Hessian with applications to the Monge-Ampère equation

DOI10.1016/j.cam.2013.12.027zbMath1301.65124OpenAlexW2041731822MaRDI QIDQ2252421

Michael Neilan

Publication date: 17 July 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2013.12.027

zbMATH Keywords

convergence analysisfinite elementMonge-Ampèrediscrete Hessian

Mathematics Subject Classification ID

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 (16)

Erratum to: ``Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D ⋮ Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation ⋮ \(C^{1}\) quintic splines on domains enclosed by piecewise conics and numerical solution of fully nonlinear elliptic equations ⋮ Unnamed Item ⋮ A C⁰ linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients ⋮ Error estimation for second‐order <scp>partial differential equations</scp> in nonvariational form ⋮ Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D ⋮ Hessian recovery for finite element methods ⋮ Adaptive \(C^0\) interior penalty methods for Hamilton-Jacobi-Bellman equations with cordes coefficients ⋮ A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems ⋮ Optimal-Transport--Based Mesh Adaptivity on the Plane and Sphere Using Finite Elements ⋮ A recovery-based linear \(C^0\) finite element method for a fourth-order singularly perturbed Monge-Ampère equation ⋮ Unnamed Item ⋮ یک الگوریتم سه مرحلهای با دقت فوقبهینه برای حل معادلات برگرز-هاکسلی وبرگرز-فیشر در حالت کلی ⋮ A convexity enforcing \(C^0\) interior penalty method for the Monge-Ampère equation on convex polygonal domains ⋮ Spline element method for Monge-Ampère equations

Uses Software

• COMSOL

Cites Work

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