Robustness of error estimates for phase field models at a class of topological changes

DOI10.1016/j.cma.2014.11.005zbMath1423.35230OpenAlexW2007801959MaRDI QIDQ1736990

Sören Bartels

Publication date: 26 March 2019

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.11.005

zbMATH Keywords

stabilitysingularitiesscalingAllen-Cahn Equationnumerical approximation spectral estimate

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Structured surfaces and interfaces, coexistent phases (74A50) Stefan problems, phase changes, etc. (80A22) Thermal effects in solid mechanics (74F05) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)

Cites Work

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• A posteriori error analysis for time-dependent Ginzburg-Landau type equations
• Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen–Cahn and Ginzburg–Landau Equations Past Topological Changes
• Spectrum for the allen-chan, chan-hillard, and phase-field equations for generic interfaces
• Geometrical Evolution of Developed Interfaces
• A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality

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