In this paper, we derive non-dissipative stable and entropy satisfying finite volume schemes for scalar PDEs. It is based on the previous analysis of [20], which deals with general reconstruction schemes. More precisely, we develop discontinuous-in-cell reconstruction schemes, based on a discontinuous reconstruction of the solution in each cell of the mesh at each time step. The intend is to ha...

Synthetic Aperture Radar (SAR) and optical images contain different types of land cover information. Moreover, whereas like-polarisation SAR images are predominately influenced by surface backscattering properties, the volume backscattering characteristics of surfaces are well represented by SAR cross-polarisation data. Hence, combined use of likeand cross-polarisation data could enhance the la...

and Applied Analysis 3 For any u(x) ∈ W 2 [0, +∞), let ⟨u(x), ψ i (x)⟩ = 0, i = 1, 2, . . ., which means that ⟨u (x) , (L ∗ φ i (x)⟩ = ⟨Lu (⋅) , φ i (⋅)⟩ = (Lu) (x i ) = 0. (12) Note that {x i } ∞ i=1 is dense in [0, +∞); therefore,Lu(x) = 0. It follows that u(x) ≡ 0 from the existence ofL. 3.1. Construction the of Iterative Sequence ?̃? n (x) and Ṽ n (x). Next we construct the iterative sequenc...

For periodic Toda chains with a large number N of particles we consider states which are N−2-close to the equilibrium and constructed by discretizing arbitrary given C2−functions with mesh size N−1. Our aim is to describe the spectrum of the Jacobi matrices LN appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H± – such op...

We present in this paper a pressure correction scheme for barotropic compressible NavierStokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, bot...

We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations...