Error estimate of the finite volume scheme for the Allen-Cahn equation

DOI10.1007/s10543-017-0687-4zbMath1397.65153OpenAlexW2763139309MaRDI QIDQ1647667

Pavel Strachota, Michal Beneš

Publication date: 26 June 2018

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-017-0687-4

zbMATH Keywords

finite volume methodisotropic materialphase transitionsolidificationerror estimatesemidiscrete schememicrostructure growthAllen-Cahn equation

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Crystals in solids (74N05) PDEs in connection with mechanics of deformable solids (35Q74) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations ⋮ A modified finite volume element method for solving the phase field Allen-Cahn model ⋮ Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation

Cites Work

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• Diffuse-interface treatment of the anisotropic mean-curvature flow.
• On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth
• Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
• Computation of three dimensional dendrites with finite elements
• Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion
• An adaptive, multilevel scheme for the implicit solution of three-dimensional phase-field equations
• An adaptive finite element method for two-phase Stefan problems in two space dimensions. I. Stability and error estimates
• An Adaptive Finite Element Method for Two-Phase Stefan Problems in Two Space Dimensions. II: Implementation and Numerical Experiments
• Convergence Analysis of Finite Volume Scheme for Nonlinear Tensor Anisotropic Diffusion in Image Processing
• Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
• Quantitative phase-field modeling of dendritic growth in two and three dimensions
• Mathematical analysis of phase-field equations with numerically efficient coupling terms