Two simple derivations of universal bounds for the C.B.S. inequality constant

summary:Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations

Finite element approximation of multi-scale elliptic problems using patches of elements

In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. This paper provides proofs of the results published earlier (see C. R. Acad. Sci. Paris, Ser. I 337 (2003) 679-684), gives a generalization of the latter to more than two domains and contains extensive numerical illustrations. New results including the spectral analysis of the iteration operator and a numerical method to evaluate the constant of the strengthened Cauchy-Buniakowski-Schwarz inequality are presente

Adaptive algorithms for partial differential equations with parametric uncertainty

In this thesis, we focus on the design of efficient adaptive algorithms for the numerical approximation of solutions to elliptic partial differential equations (PDEs) with parametric inputs. Numerical discretisations are obtained using the stochastic Galerkin Finite Element Method (SGFEM) which generates approximations of the solution in tensor product spaces of finite element spaces and finite-dimensional spaces of multivariate polynomials in the random parameters. Firstly, we propose an adaptive SGFEM algorithm which employs reliable and efficient hierarchical a posteriori energy error estimates of the solution to parametric PDEs. The main novelty of the algorithm is that a balance between spatial and parametric approximations is ensured by choosing the enhancement associated with dominant error reduction estimates. Next, we introduce a two-level a posteriori estimate of the energy error in SGFEM approximations. We prove that this error estimate is reliable and efficient. Then we provide a rigorous convergence analysis of the adaptive algorithm driven by two-level error estimates. Four different marking strategies for refinement of stochastic Galerkin approximations are proposed and, in particular, for two of them, we prove that the sequence of energy errors computed by associated algorithms converges linearly. Finally, we use duality techniques for the goal-oriented error estimation in approximating linear quantities of interest derived from solutions to parametric PDEs. Adaptive enhancements in the proposed algorithm are guided by an innovative strategy that combines the error reduction estimates computed for spatial and parametric components of corresponding primal and dual solutions. The performance of all adaptive algorithms and the effectiveness of the error estimation strategies are illustrated by numerical experiments. The software used for all experiments in this work is available online

Environmental Impact Assessment by Green Processes

Primary energy consumption around the world has been increasing steadily since the Industrial Revolution and shows no signals of slowing down in the coming years. This trend is accompanied by the increasing pollutant concentration on the Earth’s biosystems and the general concerns over the health and environmental impacts that will ensue. Air quality, water purity, atmospheric CO2 concentration, etc., are some examples of environmental parameters that are degrading due to human activities. These ecosystems can be safeguarded without renouncing industrial development, urban and economic development through the use of low environmental impact technologies instead of equivalent pollutant ones or through the use of technologies to mitigate the negative impact of high emissions technologies. Pollutant abatement systems, carbon capture technologies, biobased products, etc. need to be established in order to make environmental parameters more and more similar to the pre-industrialization values of the planet Earth. In 15 papers international scientists addressed such topics, especially combining a high academic standard coupled with a practical focus on green processes and a quantitative approach to environmental impacts

Перспективы развития фундаментальных наук: сборник научных трудов XI Международной конференция студентов и молодых ученых, г. Томск, 22-25 апреля 2014 г.

Сборник содержит труды участников XI Международной конференции студентов и молодых учёных "Перспективы развития фундаментальных наук". Включает доклады студентов и молодых ученых, представленные на секциях "физика", "химия", "математика", "технология", наноматериалы и нанотехнологии», "IT-технологии и электроника". В рамках секций представлены доклады студентов представленные для соискания стипендий по программе У.М.Н.И.К. Сборник представляет интерес для студентов, аспирантов, молодых ученых, преподавателей в области естественных наук и высшей математик

Перспективы развития фундаментальных наук: сборник научных трудов XI Международной конференция студентов и молодых ученых, г. Томск, 22-25 апреля 2014 г.

Сборник содержит труды участников XI Международной конференции студентов и молодых учёных "Перспективы развития фундаментальных наук". Включает доклады студентов и молодых ученых, представленные на секциях "физика", "химия", "математика", "технология", наноматериалы и нанотехнологии», "IT-технологии и электроника". В рамках секций представлены доклады студентов представленные для соискания стипендий по программе У.М.Н.И.К. Сборник представляет интерес для студентов, аспирантов, молодых ученых, преподавателей в области естественных наук и высшей математик