The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The sch...

It is still an open problem to prove a priori error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain Ω in IR2 and we can prove such kind ...

A family of moment-conserving advection schemes in 1-D was introduced by van Leer in the mid 1970s. Of these, MUSCL advection is the best known. That advection scheme represents the advected function, which we will call a , by a linear function within each grid cell. The linear function is determined by the values of the first two moments of this density distribution within the cell, namely the...

We deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms. We suppose that the source term is dissipative but it is not necessarily a Lipschitzian function. The convergence of the approximate solution towards the entropy solution is established for first and second order accurate MUSCL and for splitting semi-implicit met...

Inference of gene interaction networks from expression data usually focuses on either supervised or unsupervised edge prediction from a single data source. However, in many real world applications, multiple data sources, such as microarray and ISH (in situ hybridization) measurements of mRNA abundances, are available to offer multiview information about the same set of genes. We propose ISH to ...

As large-scale techniques for studying and measuring gene expressions have been developed, automatically inferring gene interaction networks from expression data has emerged as a popular technique to advance our understanding of cellular systems. Accurate prediction of gene interactions, especially in multicellular organisms such as Drosophila or humans, requires temporal and spatial analysis o...

We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using classical MUSCL-Hancock as fallback scheme. It delivers very accurate solutions in smooth regions of flow, while capturing sharp discontinuities without spurious oscillations. exploit strict equivalence between SD and Finite-Volume (FV) based on...