In this study, we derive error estimates for time accurate wavelet based schemes in two stages. First we look at the semi-discrete boundary value problem as a Cauchy problem and use spectral decomposition of self adjoint operators to arrive at the temporal error estimates both in L2 and energy norms. Later, following the wavelet approximation theory, we propose spatial error estimates in L2 and...

We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...

We prove Strichartz estimates for the kinetic transport equation employing the techniques of Keel and Tao [11] and Foschi [8]. Our results extend considerably the range of the known Strichartz estimates in the literature for that equation. We show sharpness to most of the estimates that we prove. In particular, in one spatial dimension we find the full range of validity of the Strichartz estima...

This study analyzes homicide incidence per municipality (county) in Brazil in the year 2008. The authors estimate and compare homicide rates according to different methods, finding evidence that depending on the method employed, the results can differ significantly, especially for small municipalities. Bayesian spatial procedures were employed, allowing minimization of variation in the rate est...