We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [20], [24]. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for suc...

When multilevel finite element spaces are not nested, different intergrid transfer operators would lead to different multigrid algorithms. It is proposed in this paper that discontinuous functions be averaged to continuous functions and that the bubble functions be discarded in the multigrid transferring. Applications of the techniques to various problems are presented with convergence analysis...

We present a detailed analysis of the QCD partition function in the Grand Canonical formalism. Using the fugacity expansion we find evidence for numerical instabilities in the standard evaluation of its coefficients. We discuss the origin of this problem and propose an issue to it. The correct analysis shows no evidence for a discontinuity in the baryonic density in the strong coupling limit. T...

In a recent work J. Sci. Comput. 16 (2001), 479-524, B. Despr es and F. Lagouti ere introduced a new approach to derive numerical schemes for hyperbolic conservation laws. Its most important feature is the ability to perform an exact resolution for a single traveling discontinuity. However their scheme is not entropy satisfying and can keep nonentropic discontinuities. The purpose of our work i...

We make the case that ERP-related profitability improvements first manifest themselves in gross margin. Using regression discontinuity analysis, we compared “SAP Successes” with their matched competitors before and after their SAP implementation periods and found that the gross margin of SAP successes improved significantly but not their operating margin. These results proved robust across two ...

We propose new discontinuous finite element methods that can be applied to one-dimensional elliptic problems with discontinuous coefficients. These methods are based on a class of higher degree immersed finite element spaces and can be used with a mesh independent of the location of coefficient discontinuity. Numerical experiments are presented to show that these methods can achieve optimal con...

We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has O(∆x) errors, improving over O(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assert...

The stabilization of high order spectral elements to solve the transport equations for tracers in the atmosphere remains an active topic of research among atmospheric modelers. This paper builds on our previous work on variational multiscale stabilization (VMS) and discontinuity capturing (DC) [Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equa...

A key issue in the creation of error-free tool path for numerically controlled (NC) surface machining is gouging (over-cut> prevention. In the case of solid-based machining, where the creation of tool paths across several surfaces in a single pass is imperative, the major sources for gouging are the tangent discontinuity (C’ discontinuity) and the surface gap (Co discontinuity) occurred in the ...

In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right-hand sides of Filippov type. In particular: (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and non-ambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and i...