Rates of Convergence in $W^2_p$-Norm for the Monge--Ampère Equation

DOI10.1137/17M1160409zbMath1403.65115arXiv1712.02492OpenAlexW2963685923MaRDI QIDQ4554048

Michael Neilan, Wujun Zhang

Publication date: 7 November 2018

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

Full work available at URL: https://arxiv.org/abs/1712.02492

zbMATH Keywords

Monge-Ampère equation\(W^2_p\) error estimatediscrete Alexandroff maximum principle

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Maximum principles in context of PDEs (35B50) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06) Weak solutions to PDEs (35D30) Monge-Ampère equations (35J96)

Related Items (5)

Optimal Pointwise Error Estimates for Two-Scale Methods for the Monge--Ampère Equation ⋮ A note on the Monge–Ampère type equations with general source terms ⋮ Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport ⋮ On the weak convergence of Monge-Ampère measures for discrete convex mesh functions ⋮ A convexity enforcing \(C^0\) interior penalty method for the Monge-Ampère equation on convex polygonal domains

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