PERONA-MALIK EQUATION - ERROR ESTIMATES FOR EXPLICIT FINITE VOLUME SCHEME
نویسندگان
چکیده
منابع مشابه
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
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We consider the Cauchy problem for the Perona-Malik equation ut = div ( ∇u 1 + |∇u|2 ) in a bounded open set Ω ⊆ R, with Neumann boundary conditions. If n = 1, we prove some a priori estimates on u and ux. Then we consider the semi-discrete scheme obtained by replacing the space derivatives by finite differences. Extending the previous estimates to the discrete setting we prove a compactness re...
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متن کاملAn Analysis of the Perona-Malik Scheme
We investigate how the Perona-Malik scheme evolves piecewise smooth initial data in one dimension. By scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size, we obtain a meaningful continuum limit. The resulting evolution can be seen as the gradient flow for an energy, just as the discrete evolutions are gradient flows for discrete energies. I...
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A new technique for the implementation of cell-centered finite volume schemes is proposed. It is based on an equivalence between these schemes and the non-conforming Crouzeix-Raviart finite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two significant advantages that make it attractive. On the one hand the resulting formulation is well-def...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2005
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2005.9637293