We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long-time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete comparison functions. Despite the equation having a region where it is backward parabolic, we prove a discrete comparison principle, which is the key tool for the convergence result.
Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension
NOVAGA, MATTEO;
2011
Abstract
We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long-time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete comparison functions. Despite the equation having a region where it is backward parabolic, we prove a discrete comparison principle, which is the key tool for the convergence result.File in questo prodotto:
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