Convergence of discrete schemes for the Perona-Malik equation

DOI10.1016/j.jde.2008.05.003zbMath1155.35002OpenAlexW2069193207MaRDI QIDQ935126

C. Tornese, Giovanni Bellettini, Maurizio Paolini, Matteo Novaga

Publication date: 31 July 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.05.003

zbMATH Keywords

periodic boundary conditionsimage reconstructionone space dimensionfull discretizationforward-backward parabolic equationssemidiscretizations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Network design and communication in computer systems (68M10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theoretical approximation in context of PDEs (35A35)

Related Items

Diffusion, pre-smoothing and gradient descent ⋮ Classification of equilibria and \(\Gamma \)-convergence for the discrete Perona-Malik functional ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ Motion and pinning of discrete interfaces ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ An Example of Global Classical Solution for the Perona-Malik Equation ⋮ Applications of approximate gradient schemes for nonlinear parabolic equations.

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