SHARP ERROR ANALYSIS FOR CURVATURE DEPENDENT EVOLVING FRONTS

DOI10.1142/S0218202593000369zbMath0802.65124OpenAlexW2023218984MaRDI QIDQ4300118

Claudio Verdi, Maurizio Paolini, Ricardo H. Nochetto

Publication date: 11 December 1994

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202593000369

zbMATH Keywords

asymptoticsphase transitionspattern formationcombustionerror estimatediffusion equationsflame propagationsmall positive parametercurvature dependent evolving frontssingularity perturbed parabolic double obstacle problem

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Stefan problems, phase changes, etc. (80A22) Error bounds for boundary value problems involving PDEs (65N15) Combustion (80A25) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05) Initial value problems for second-order parabolic equations (35K15)

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Quadratic rate of convergence for curvature dependent smooth interfaces: A simple proof ⋮ Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. ⋮ APPROXIMATION AND COMPARISON FOR NONSMOOTH ANISOTROPIC MOTION BY MEAN CURVATURE IN ℝ^N ⋮ A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem ⋮ The limit of the anisotropic double-obstacle Allen–Cahn equation ⋮ Error estimates and numerical simulations of mean curvature flow through a modified reaction-diffusion equation

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