Tadmor, Nezzar and Vese [Eitan Tadmor, Suzanne Nezzar, and Luminita Vese. A multiscale image representation using hierarchical (BV, L2) decompositions. Multiscale Model. Simul., 2(4):554–579, 2004.] developed a total variation based multiscale method for decomposing a function f ∈ BV into a countable set of features {uk : k = 0, 1, 2 . . .} associated to a sequence of dyadic scales {λk = λ02−k ...

Entropy solutions have beenwidely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (AnnMath 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical sc...

In this work we compare two semidiscrete schemes for the solution of hy-perbolic conservation laws, namely the relaxation [JX95] and the Kurganov Tadmor central scheme [KT00]. We are particularly interested in their behavior under small time steps, in view of future applications to convection diffusion problems. The schemes are tested on two benchmark problems, with one space variable. 1 Motiva...

We study the global well-posedness of Euler--Monge--Ampère (EMA) system. obtain a sharp, explicit critical threshold in space initial configurations which guarantees regularity EMA system with radially symmetric data. The result is obtained using two independent approaches---one spectral dynamics Liu and Tadmor [Comm. Math. Phys., 228 (2002), pp. 435--466] other based on geometric approach Bren...

Drought is a serious threat for sustainable agriculture. Barley represents a species well adapted to environmental stresses including drought. To elucidate the adaptive mechanism of barley on transcriptional level we evaluated transcriptomic changes of two contrasting barley cultivars upon drought using the microarray technique on the level of leaves and crowns. Using bioinformatic tools, diffe...

The central scheme of Nessyahu and Tadmor (J. Comput. Phys, 87(1990)) has the benefit of not having to deal with the solution within the Riemann fan for solving hyperbolic conservation laws and related equations. But the staggered averaging causes large dissipation when the time step size is small comparing to the mesh size. The recent work of Kurganov and Tadmor (J. Comput. Phys, 160(2000)) ov...

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...

In [1] and some following publications, Tadmor and Gelb took up a well known property of conjugate Fourier series in 1-d, namely the property to detect jump discontinuities in given spectral data. In fact, this property of conjugate series is known for quite a long time. The research in papers around the year 1910 shows that there were also other means of detecting jumps observed and analysed. ...

We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov an...

We present a new family of high-resolution, nonoscillatory semidiscrete central schemes for the approximate solution of the ideal magnetohydrodynamics (MHD) equations. This is the second part of our work, where we are passing from the fully discrete staggered schemes in [J. Balbás, E. Tadmor, and C.-C. Wu, J. Comput. Phys., 201 (2004), pp. 261–285] to the semidiscrete formulation advocated in [...