Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems

We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of L∞(0, T; L2(Ω)) and the higher order spaces, L∞(0, T;H1(Ω)) and H1(0, T; L2(Ω)), with optimal orders of convergence

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition

We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this system in the case when both the microstructure and macroscopic domain are two-dimensional. The main difficulty is created by the presence of a boundary nonlinear term entering the transmission condition. Besides using the particular two-scale structure of the system, the ingredients of the proof include two-scale interpolation-error estimates, an interpolation-trace inequality, and improved regularity estimates.Comment: 14 pages, table of content

A comparison of duality and energy aposteriori estimates for L?(0,T;L2({\Omega})) in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove aposteriori error estimates for fully discrete back- ward Euler scheme for linear parabolic equations. As an application, we com- bine our result with the residual based estimators from the aposteriori esti- mation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the L \infty (0, T ; L2({\Omega})) norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson (1991) by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estima- tors. For comparison with previous results we derive also an energy-based aposteriori estimate for the L \infty (0, T ; L2({\Omega}))-error which simplifies a previous one given in Lakkis and Makridakis (2006). We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.Comment: 30 pages, including 7 color plates in 4 figure

Distribution of phytobenthos along the coast of Lebanon

A phytosociological study of the phytobenthos was carried out along the coast of Lebanon during 1996-97. Samples were collected seasonally at six sites, some of which showed distinct pollution signature. Quadrates of 0.04 m-2 were taken at selected stations fixed on transects perpendicular to the rocky shore and covering the supralittoral, the mediolittoral and infralittoral zones. The taxonomic composition, the abundance and species diversity of algal community were analysed in relation to environmental factors. A total of 230 taxa were identified during the period of survey. Several sources of pollution, resulted in the reduction of macroalgae biomass and of the taxonomic diversity. Several Indo-Pacific species were found within the different phytocoenoses of the area; most of them were introduced into the Levantine Basin through the Suez Canal. These species, that were introduced into the Eastern Mediterranean, formed permanent populations; some of them were highly spread and dominated over other endemic species or even they replaced them

A posteriori L∞(L^2)-error bounds in finite element approximation of the wave equation

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Some Sampling Designs and Estimation Problems

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe. In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for investigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spatial systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population with one dimension, and we derive in general these estimators for n-dimensional population. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions are derived

Arab Regional Integration:: A neo-functionalist and transactionalist analysis

This thesis is a multidisciplinary analysis of Arab regional integration using the neo- functionalist and transactionalist approaches to integration. Neo-functionalism analyses the process of integration in the Arab World by studying the role of regional institutions including the league of Arab States and three Arab joint ventures. The transactionalist approach examines the impact of regional trade on political and economic integration in the Arab Mashreq. The analysis of the Arab joint ventures is taken further by using elements of business and finance theories. It is conducted on two different levels: the first analyses the operational and financial performance of these ventures. The second examines their role in promoting regional integration especially in the sectors concerned. The analysis is intended to find out whether these ventures were commercially viable or were more politically inspired. Qualitative information was collected from conducting constructive interviews with Arab economists, politicians and managers of the Arab joint ventures examined. The quantitative data was collected from recognisable resources including the Economic and Social Commission for Western Asia and the Arab Monetary Fund. The problems encountered in this thesis resulted from the application of these theoretical approaches to integration, which are designed to study integration in politically developed societies with more advanced economies. However, the choice is justified since there are no alternatives. Secondly, the data on trade and Arab joint ventures may not be completely accurate since it does not record all transactions. The thesis concludes the following: at the political level, regional institutions did not promote Arab integration since they lacked aspects of supranationality and collective decision-making processes. Also, they did not affect the Arab elite's attitudes and could not initiate a viable process of integration that would spill over from one sector to another. At the economic level, the low level of regional trade in the Arab Mashreq did not prevent the occurrence of many attempts at Arab integration. Moreover, the Arab joint ventures were more politically inspired than commercially. Although they were more resilient to economic and political instability in the Arab World, their role in promoting regional integration was limited