A convergent monotone difference scheme for motion of level sets by mean curvature

DOI10.1007/s00211-004-0566-1zbMath1070.65082OpenAlexW2089633435MaRDI QIDQ706598

Adam M. Oberman

Publication date: 8 February 2005

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-004-0566-1

zbMATH Keywords

monotonicitystabilityconvergenceconsistencydegenerate nonlinear parabolic equationimage processingaccuracycombustionlattice pointsdifferential geometrynumerical experimentfront propagationrotation invariancedegenerate elliptic equationfluid dynamicsregularity of solutionsstencildirectional resolutionexplicit convergent finite difference schememotion of level sets by mean curvature

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Degenerate elliptic equations (35J70) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items

Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. ⋮ Nonlinear projection recovery in digital inpainting for color image restoration ⋮ Semi-implicit Alternating Discrete Duality Finite Volume Scheme for Curvature Driven Level Set Equation ⋮ Flux-based level set method: A finite volume method for evolving interfaces ⋮ The flexible, extensible and efficient toolbox of level set methods ⋮ A novel method for the numerical solution of a hybrid inverse problem of electrical conductivity imaging ⋮ Cell-Centered Finite Volume Method for Regularized Mean Curvature Flow on Polyhedral Meshes ⋮ COMPUTING THE CONVEX ENVELOPE USING A NONLINEAR PARTIAL DIFFERENTIAL EQUATION ⋮ A semi-Lagrangian scheme for the game \(p\)-Laplacian via \(p\)-averaging ⋮ Computing the level set convex hull ⋮ Mean curvature, threshold dynamics, and phase field theory on finite graphs ⋮ Asymptotic statistical characterizations of \(p\)-harmonic functions of two variables ⋮ Statistical Functional Equations and p-Harmonious Functions ⋮ A deterministic-control-based approach to fully nonlinear parabolic and elliptic equations ⋮ Finite difference methods for the infinity Laplace and \(p\)-Laplace equations ⋮ Numerical Solution of a Regularized Weighted Mean Curvature Flow Problem For Electrical Conductivity Imaging ⋮ Unnamed Item ⋮ A Brief Survey on Semi-Lagrangian Schemes for Image Processing ⋮ Statistical exponential formulas for homogeneous diffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Motion of level sets by mean curvature. I
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Motion of multiple junctions: A level set approach
• Level set methods and dynamic implicit surfaces
• Convergent difference schemes for nonlinear parabolic equations and mean curvature motion
• User’s guide to viscosity solutions of second order partial differential equations
• Phase transitions and generalized motion by mean curvature
• Geometric Level Set Methods in Imaging, Vision, and Graphics
• A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
• Algorithms for Computing Motion by Mean Curvature
• Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems
• On the Approximation of Linear Elliptic Differential Equations by Difference Equations with Positive Coefficients
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations