Optimal Pointwise Error Estimates for Two-Scale Methods for the Monge--Ampère Equation

DOI10.1137/18M1165670zbMath1397.65278OpenAlexW2811321764MaRDI QIDQ4572027

Wenbo Li, Ricardo H. Nochetto

Publication date: 4 July 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1165670

zbMATH Keywords

monotonesemi-Lagrangian methodpointwise error estimatesMonge-Ampèretwo-scale methodHölder and Sobolev regularity

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) Finite difference methods for boundary value problems involving PDEs (65N06) Monge-Ampère equations (35J96)

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Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions, Numerical methods for fully nonlinear and related PDEs. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting), Convergent Two-Scale Filtered Scheme for the Monge--Ampère Equation, Second order monotone finite differences discretization of linear anisotropic differential operators, A convexity enforcing \(C^0\) interior penalty method for the Monge-Ampère equation on convex polygonal domains, Two-scale methods for convex envelopes

Cites Work

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• Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations
• An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic Monge-Ampère equation in two dimensions
• Two remarks on Monge-Ampère equations
• On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I
• Discrete ABP estimate and convergence rates for linear elliptic equations in non-divergence form
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes
• Finite element approximations of the three dimensional Monge-Ampère equation
• Standard finite elements for the numerical resolution of the elliptic Monge–Ampère equation: classical solutions
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge–Ampère Equation in Dimensions Two and Higher
• ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS
• Discretization of the 3d monge−ampere operator, between wide stencils and power diagrams
• Mixed Finite Element Methods for the Fully Nonlinear Monge–Ampère Equation Based on the Vanishing Moment Method
• On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Rates of Convergence in $W^2_p$-Norm for the Monge--Ampère Equation
• Two-scale method for the Monge-Ampère equation: Convergence to the viscosity solution
• Convergent Semi-Lagrangian Methods for the Monge--Ampère Equation on Unstructured Grids
• The Mathematical Theory of Finite Element Methods
• Monotone and consistent discretization of the Monge-Ampère operator
• The Monge-Ampère equation