Quadratic finite element approximations of the Monge-Ampère equation

DOI10.1007/s10915-012-9617-4zbMath1272.65094OpenAlexW2009553465MaRDI QIDQ1936318

Michael Neilan

Publication date: 4 February 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-012-9617-4

zbMATH Keywords

convergencefinite element methodNewton's methodnumerical experimentsDirichlet boundary value problemquasi-optimal error estimatesfully nonlinear Monge-Ampère equationlocalized pointwise error estimates

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Monge-Ampère equations (35J96)

Related Items (14)

Erratum to: ``Quadratic mixed finite element approximations of the Monge-Ampère equation in 2D ⋮ Discretization of the 3d monge−ampere operator, between wide stencils and power diagrams ⋮ A multigrid scheme for 3D Monge–Ampère equations ⋮ Rates of Convergence in $W^2_p$-Norm for the Monge--Ampère Equation ⋮ Convergence analysis of a finite element method for second order non-variational elliptic problems ⋮ A C⁰ linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients ⋮ Numerical analysis of strongly nonlinear PDEs ⋮ A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form ⋮ Pointwise rates of convergence for the Oliker-Prussner method for the Monge-Ampère equation ⋮ Finite element methods for second order linear elliptic partial differential equations in non-divergence form ⋮ Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic pdes ⋮ Unnamed Item ⋮ 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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