We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Gamma-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.
Finite Difference Approximation of Free Discontinuity Problems
Mora, M. G.
2001-01-01
Abstract
We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Gamma-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.File in questo prodotto:
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