In this paper, we consider convergence of classical high order Godunov-type schemes towards entropy solutions for scalar conservation laws. It is well known that sufficient conditions for such convergence include total variation boundedness of the reconstruction and cell or wavewise entropy inequalities. We prove that under large time steps, we only need total variation boundedness of the recon...

This paper studies the total variation regularization model with an L1 fidelity term (TV-L1) for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry subproblems. Using this result we show that the TV-L1 model is able to separate image features according to their scales,...

We show that any conservative scheme for solving scalar conservation laws in two space dimensions, which is total variation diminishing, is at most first-order accurate.

Let Ω be an open subset of R where 2 ≤ n ≤ 7; we assume n ≤ 2 because the case n = 1 has been treated elsewhere (see [Alli]) and is quite different from the case n > 1; we assume n ≤ 7 is that our work will make use of the regularity theory for area minimizing hypersurfaces. Let F(Ω) = L1(Ω) ∩ L∞(Ω)). Suppose s ∈ F(Ω) and Suppose γ : R→ [0,∞) is locally Lipschitzian, positive on R ∼ {0} and zer...

We construct an interpolation operator that does not increase the total variation and is defined on continuous first degree finite elements over Cartesian meshes for any dimension d and right triangular meshes for d = 2. The operator is stable and exhibits second order approximation properties in any Lp, 1 ≤ p ≤ ∞. With the help of it we provide improved error estimates for discrete minimizers ...

In this paper we describe a process used for conceiving new products for the Brazilian interactive TV platform. Considering all the restrictions and many aspects of context and usage, we proposed and refined an interaction design process. This process was applied to design three new interactive products. To capture details from context, the process started with intensive qualitative research in...