Discontinuous velocity boundary data for the lid driven cavity flow has long been causing difficulties in both theoretical analysis and numerical simulations. In finite element methods, the variational form for the driven cavity flow is not valid since the velocity is not in H. Hence standard error estimates do not work. By using only W1,r (1 < r < 2) regularity and constructing a continuous ap...

In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in R2, the method is shown to converge at a rate 0(hn+l) when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

Gascuel, O. and G. Caraux, Distribution-free performance bounds with the resubstitution error estimate, Pattern Recognition Letters 13 (1992) 757-764. Two distribution-free upper bounds are given for the true error rate of a classifier, using the resubstitution error estimate. These bounds apply when the classifier is selected from a finite decision rule set. Both improve a bound proposed by Va...

A method for finding all matches in a pre-processed dictionary for a query string q and with at most k differences is presented. A very fast constant-time estimate using hashes is presented. A tree structure is used to minimise the number of estimates made. Practical tests are performed, showing that the estimate can filter out 99% of the full comparisons for 40% error rates and dictionaries of...

We report an error estimate of the multi-dimensional fast Gauss transform (FGT), which is much sharper than that previously reported in the literature. An application to the Karhunen–Loeve decomposition in the three-dimensional physical space is also presented that shows savings of three orders of magnitude in time and memory compared to a direct solver. 2006 Elsevier Inc. All rights reserved.

A computable error bound for mixed finite element methods is established in the model case of the Poisson–problem to control the error in the H(div,Ω) ×L2(Ω)–norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart–Thomas, Brezzi-Douglas-Marini, and Brezzi-DouglasFortin-Marini elements. 1. Mixed method for the Poisson problem Mixed finite element methods are well-e...

the statistical analysis of spatial data is usually done under gaussian assumption for the underlying random field model. when this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. one of the crucial problems in this setting is specifying the block sizes. in this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...