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We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are obtained: (i) Stability of an associated ODE implies that the stochastic recursion is stable in a strong sense when a gain(More)
In this paper, we focus on error estimates to smooth solutions of semi-discrete discontin-uous Galerkin (DG) methods with quadrature rules for scalar conservation laws. The main techniques we use are energy estimate and Taylor expansion first introduced by Zhang and Shu in [24]. We show that, with P k (piecewise polynomials of degree k) finite elements in(More)
This paper addresses how to manage planar spatial data using MongoDB, a popular NoSQL database characterized as a document-oriented, rich query language and high availability. The core idea is to flatten a hierarchical R-tree structure into a tabular MongoDB collection, during which R-tree nodes are represented as collection documents and R-tree pointers(More)
In this work, we propose an interfacial scheme accompanying the lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, including conjugate conditions with or without jumps in heat and mass transfer, continuity of macroscopic variables and normal fluxes in ion diffusion in porous media with different porosity, and(More)
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