Improved Accuracy of Monotone Finite Difference Schemes on Point Clouds and Regular Grids

DOI10.1137/18M1200269zbMath1481.65204arXiv1807.05150OpenAlexW2980537460MaRDI QIDQ5240803

Chris Finlay, Adam M. Oberman

Publication date: 29 October 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05150

zbMATH Keywords

finite differencesstability and convergencenonlinear degenerate elliptic partial differential equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Degenerate elliptic equations (35J70) Second-order elliptic equations (35J15) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (5)

A convergence framework for optimal transport on the sphere ⋮ Boundary estimation from point clouds: algorithms, guarantees and applications ⋮ Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation ⋮ Convergence Framework for the Second Boundary Value Problem for the Monge--Ampère Equation ⋮ Convergent finite difference methods for fully nonlinear elliptic equations in three dimensions

Uses Software

• Mulprec
• DistMesh

Cites Work

• Unnamed Item
• Adaptive, anisotropic and hierarchical cones of discrete convex functions
• Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemes
• Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian
• Classes of graphs which approximate the complete Euclidean graph
• Meshfree finite difference approximations for functions of the eigenvalues of the Hessian
• Monotone mixed finite difference scheme for Monge-Ampère equation
• Sparse non-negative stencils for anisotropic diffusion
• On the numerical solution of a two-dimensional Pucci's equation with Dirichlet boundary conditions: a least-squares approach
• Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries
• Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction
• The convex envelope is the solution of a nonlinear obstacle problem
• Numerical Methods in Scientific Computing, Volume I
• COMPUTING THE CONVEX ENVELOPE USING A NONLINEAR PARTIAL DIFFERENTIAL EQUATION
• User’s guide to viscosity solutions of second order partial differential equations
• Two-scale method for the Monge-Ampère equation: Convergence to the viscosity solution
• High-order filtered schemes for time-dependent second order HJB equations
• Numerical analysis of strongly nonlinear PDEs
• A Simple Mesh Generator in MATLAB
• Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
• Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems
• Monotone and consistent discretization of the Monge-Ampère operator

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