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 prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any Lipschitz continuous monotone Φ : R→ R, we have that |Φ(u)|TV (R) is nonincreasing in time. We call this property Total Oscillation Diminishing because it is in contradiction with the oscillations observed recently on some numerical computations based on TVD ...

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...

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.

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...

We prove that isentropic gas flow does not admit non-degenerate TVD fields on any invariant set M(r0, s0) = {r0 < r < s < s0}, where r, s are Riemann coordinates. A TVD field refers to a scalar field whose spatial variation VarX(φ(τ(t,X), u(t,X))) is nonincreasing in time along entropic solutions. The result is established under the assumption that the Riemann problem defined by an overtaking s...

The one–dimensional differential equations for the conservation mixture mass and mixture momentum coupled by a relative velocity conservation equation have been solved for an isentropic mixture of gas and liquid two–phase flow. Under certain restrictions the resulting system of partial differential equations is hyperbolic and allow discontinuous solutions. These equations have been solved by th...

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 investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...