scientific article; zbMATH DE number 696935
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Publication:4313792
zbMath0886.35079MaRDI QIDQ4313792
Claudio Verdi, Ricardo H. Nochetto, Maurizio Paolini
Publication date: 10 May 1998
Full work available at URL: http://www.numdam.org/item?id=ASNSP_1994_4_21_2_193_0
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Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Connections of harmonic functions with differential equations in two dimensions (31A35)
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Quadratic rate of convergence for curvature dependent smooth interfaces: A simple proof ⋮ Dynamics of interfaces in a scalar parabolic equation with variable diffusion coefficients ⋮ Numerical Surgery for Mean Curvature Flow of Surfaces ⋮ A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem ⋮ Optimal control of geometric partial differential equations ⋮ Numerical analysis of a second-order IPDGFE method for the Allen-Cahn equation and the curvature-driven geometric flow ⋮ Stability analysis for Allen-Cahn type equation associated with the total variation energy ⋮ Error estimates and numerical simulations of mean curvature flow through a modified reaction-diffusion equation ⋮ Ginzburg-Landau equation and motion by mean curvature. I: Convergence
Cites Work
- Motion of level sets by mean curvature. I
- The heat equation shrinks embedded plane curves to round points
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Generation and propagation of interfaces for reaction-diffusion equations
- Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
- Fast Reaction, Slow Diffusion, and Curve Shortening
- Phase transitions and generalized motion by mean curvature
- Front Propagation and Phase Field Theory
- Geometrical Evolution of Developed Interfaces
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