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.

Phonemic accuracy of children with cochlear implants (CI) is often reported to be lower in comparison with normally hearing (NH) age-matched children. In this study, we compare phonemic accuracy development in the spontaneous speech of Dutch-speaking children with CI and NH age-matched peers. A dynamic cost model of Levenshtein distance is used to compute the accuracy of each word token. We set...

We propose a discretization scheme for a numerical solution of elliptic PDE’s, based on local representation of functions, by their Taylor polynomials (jets). This scheme utilizes jet calculus to provide a very high order of accuracy for a relatively small number of unknowns involved.

Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. Th...

Given an ordinary differential equation on a homogeneous manifold, one can construct a “geometric integrator” by determining a compatible ordinary differential equation on the associated Lie group, using a Lie group integration scheme to construct a discrete time approximation of the solution curves in the group, and then mapping the discrete trajectories onto the homogeneous manifold using the...

Abstract. We are concerned with the detection of edges – the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our...

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on gener...

Hindi and Urdu are variants of the same language, but while Hindi is written in the Devnagri script from left to right, Urdu is written in a script derived from a Persian modification of Arabic script written from right to left. The difference in the two scripts has created a script wedge as majority of Urdu speaking people in Pakistan cannot read Devnagri, and similarly the majority of Hindi s...