Geodesic
Applications of approximate gradient schemes for nonlinear parabolic equations
Applications of Mathematics, Tome 60 (2015) no. 2, pp. 135-156.

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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.
DOI : 10.1007/s10492-015-0088-4
Classification : 35K59, 65M08, 65M12
Keywords: regularized Perona-Malik equation; gradient schemes 
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     title = {Applications of approximate gradient schemes for nonlinear parabolic equations},
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Eymard, Robert; Handlovičová, Angela; Herbin, Raphaèle; Mikula, Karol; Stašová, Olga. Applications of approximate gradient schemes for nonlinear parabolic equations. Applications of Mathematics, Tome 60 (2015) no. 2, pp. 135-156. doi : 10.1007/s10492-015-0088-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0088-4/

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