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 ...

This paper concerns the numerical schemes describing solute transport in fissured systems which are characterized by the tectonic blocks and spatial repartition of hydraulic properties with dual permeability structures composed of highand low-permeability blocks of the chalk aquifer (Northern France). Both advection and diffusion mechanisms are taken into account. The novel mathematical approac...

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...

Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for onedimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total va...

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknow...

This paper studies a family of nite volume schemes for the hyperbolic scalar conservation law ut +∇g · f(x, u) = 0 on a closed Riemannian manifold. For an initial value in BV(M) and an at most 2 -dimensional manifold we will show that these schemes converge with a h 1 4 convergence rate towards the entropy solution. When M is 1 -dimensional the schemes are TVD and we will show that this improve...

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...

Flux-vector and tlux-difference splittings for the inviscid terms of :hs compressible flc:\ equations are derived under the assumption of a general equation of state for a reai gas in squilibrium. No unnecessary assumptions. approximations, or auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and ;cadilq appi) to curvilinear coordin...

Relativistic temperature of gas raises the issue of the equation of state (EoS) in relativistic hydrodynamics. We study the EoS for numerical relativistic hydrodynamics, and propose a new EoS that is simple and yet approximates very closely the EoS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the Eo...