The convergence of a numerical method for total variation flow. (May 2021)

• Record Type: Journal Article
• Authors: Hong, Qianying; Lai, Ming-jun; Wang, Jingyue
• Is Part Of: Journal of algorithms & computational technology. Volume 15(2021)
• Publication Date: 2021-05
• Subjects: Rudin-Osher-Fatemi -- model -- Total Variation flow -- finite difference method -- numerical analysis; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/17483026211011323
• Languages: English
• ISSNs: 1748-3018

Abstract

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.