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Finite Elements
An easy-to-understand guide covering the key principles of finite element methods and its applications to differential equations.
Numerical Methods for Singularly Perturbed Differential Equations
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition...
Fluids Under Pressure
This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
Large-Scale Scientific Computing
This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Large-Scale Scientific Computations, LSSC 2003, held in Sozopol, Bulgaria in June 2003. The 50 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on preconditioning techniques, Monte Carlo methods and quasi-Monte-Carlo methods, set-value of numerics and reliable computing, environmental modeling, and large-scale computations for engineering problems.
Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed differential equations; that is, problems whose solutions exhibit boundary and/or interior layers.
Transport Processes at Fluidic Interfaces
There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings ...
Robust Numerical Methods for Singularly Perturbed Differential Equations
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Mathematics - Key Technology for the Future
Efficient transfer between science and society is crucial for their future development. The rapid progress of information technology and computer systems offers a large potential and new perspectives for solving complex problems. Mathematical modelling and simulation have become important tools not only in scientific investigations but also in analysing, planning and controlling technological and economic processes. Mathematics, imbedded in an interdisciplinary concept, has become a key technology. The book covers the results of a variety of major projects in industrial mathematics following an initiative of the German Federal Ministry of Education and Research. All projects are collaborations of industrial companies and university-based researchers, and range from automotive industry to computer technology and medical visualisation. In general, the projects presented in this volume prove that new mathematical ideas and methods can be decisive for the solution of industrial and economic problems.
Numerical Mathematics And Advanced Applications: 3rd European Conf, Jul 99, Finland
This volume contains major lectures given at ENUMATH 99, the 3rd European Conference on Numerical Mathematics and Advanced Applications.The ENUMATH conferences were established in 1995 to provide a forum for discussing current topics in numerical mathematics. They convene leading experts and young scientists, with special emphasis on contributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms, as well as their application to challenging scientific and industrial problems.The topics of ENUMATH 99 included finite element methods, a posteriori error control and adaptive mesh design, non-matching grids, least-squares methods for partial differential equations, boundary element methods and optimization in partial differential equations. Apart from theoretical aspects, a major part of the conference was devoted to numerical methods in interdisciplinary applications such as problems in computational fluid, electrodynamics, telecommunications software, as well as visualization.
BAIL 2008 - Boundary and Interior Layers
These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ̈ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research inv...
