Rate of convergence of regularization procedures and finite element approximations for the total variation flow
type: Item
instance of: scholarly article
title: Rate of convergence of regularization procedures and finite element approximations for the total variation flow
zbMATH Open document ID: 1075.65114
author: Xiaobing Feng
author: Markus von Oehsen
author: Andreas Prohl
published in: Numerische Mathematik
publication date: 2005-06-13T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11850/32943
review text: The paper deals with finite element approximations of the \(L^2\)-gradient flow for a total variational functional. In [M2AN, Math. Model. Numer. Anal. 37, No.3, 533--556 (2003; Zbl 1050.35004)] the authors proved that the solution of the regularized flow (characterized by a parameter \(\varepsilon\)) converges to the solution of the total variational flow. In this paper the authors derive the rate of the convergence. Practically useful error estimates, which depend on \(1/\varepsilon\) only in low polynomial orders, are established. Numerical examples verify the theoretical results and show the efficiency of the proposed methods.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 2175549
zbMATH Keywords: regularization procedure
zbMATH Keywords: convergence
zbMATH Keywords: finite element
zbMATH Keywords: total variation flow
zbMATH Keywords: error estimates
zbMATH Keywords: numerical examples
reviewed by: Vit Dolejsi
MaRDI profile type: Publication
OpenAlex ID: W1970734370
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DOI: 10.1007/S00211-005-0585-6
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description: scientific article; zbMATH DE number 2175549