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Applications of Mathematics

, Volume 60, Issue 2, pp 135–156 | Cite as

Applications of approximate gradient schemes for nonlinear parabolic equations

  • Robert EymardEmail author
  • Angela Handlovičová
  • Raphaèle Herbin
  • Karol Mikula
  • Olga Stašová
Article

Abstract

We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion equations.

Keywords

regularized Perona-Malik equation gradient schemes 

MSC 2010

65M08 65M12 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  • Robert Eymard
    • 1
    Email author
  • Angela Handlovičová
    • 2
  • Raphaèle Herbin
    • 3
  • Karol Mikula
    • 4
  • Olga Stašová
    • 4
  1. 1.Université Paris-EstMarne-la-Vallée, Cedex 2France
  2. 2.Department of Mathematics and Constructive GeometrySlovak University of TechnologyBratislavaSlovakia
  3. 3.Centre de Mathématiques et Informatique (CMI)Aix-Marseille UniversitéMarseille Cedex 13France
  4. 4.Department of Mathematics and Constructive GeometrySlovak University of TechnologyBratislavaSlovakia

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