Abstract. We prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any smooth function Φ, we have that Φ(u) is TVD with the correct definition of the initial seminorm. We call this property Total Oscillation Diminishing. The reason being that it is in contradiction with the oscillations observed recently on some numeri...

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminish...

In this paper we provide a method to compute explicitly the solution of the total variation denoising problem with a L fidelity term, where p > 1, for piecewise constant data in dimension one.

We apply a general procedure of the author to choose penalty parameters in total variation denoising.

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The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and Koopman (KMD) of TV-flow compare obtained modes TV spectral decomposition. We propose a computationally efficient algorithm evolve TV-flow. A significant speedup by three orders magnitude obtai...