Discontinuous Galerkin Methods

This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very quic

The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with in

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential

This monograph presents methods for time domain wave propagation problems. It also describes how to implement them in physical models. Highlights include the construction of 3D finite elements on non

Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and comput

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The boo

Replacing the Traditional Physical Model ApproachComputational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change

The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars worki

??????This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear

Rocks and soils can behave as discontinuous materials, both physically and mechanically, and for such discontinuous nature and behaviour there remain challenges in numerical modelling methods and tech

Analysis of large deformation, rigid body movement and strain or stress for discontinuous materials is often required for project designs and plans in the fields of engineering and disaster prevention

Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, r

An elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for t

A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: • Statistical fluctuation formulae for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions • High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and volume integral methods in layered media for Poisson–Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots • Absorbing and UPML boundary conditions • High-order hierarchical Nédélec edge elements • High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods • Finite element and plane wave frequency-domain methods for periodic structures • Generalized DG beam propagation method for optic

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer po

This book brings together the recent cutting-edge work on computational methods in photonics and their applications. The latest advances in techniques such as the Discontinuous Galerkin Time Domain me

A key figure in the field of evolutionary biology, William Bateson (1861–1926) revived Mendelian methods of analysis to develop Darwin's theory of evolution, thereby pioneering the study of genetics. In these lectures, published at Yale in 1913, Bateson systematically chronicles the era's conflicting and developing theories on taxonomy, speciation, variation and hybridisation, and includes his own thoughts on continuous and discontinuous variation and its causes. Drawing on the comparative physiology and anatomy of species that he knew from his wide experience, citing detailed examples from across the taxonomic kingdoms, Bateson brings to life this exciting time in biology. Because the theories central to the modern understanding of genetics, heredity and evolution were formed at this time, this work remains valuable and relevant to students of biology and the history of science.

The market for print steadily expanded throughout the eighteenth-century Atlantic world thanks to printers' efforts to ensure that ordinary people knew how to read and use printed matter. Reading is and was a collection of practices, performed in diverse but always very specific ways. These practices were spread down the social hierarchy through printed guides. Eve Tavor Bannet explores guides to six manners or methods of reading, each with its own social, economic, commercial, intellectual and pedagogical functions, and each promoting a variety of fragmentary and discontinuous reading practices. The increasingly widespread production of periodicals, pamphlets, prefaces, conduct books, conversation-pieces and fictions, together with schoolbooks designed for adults and children, disseminated all that people of all ages and ranks might need or wish to know about reading, and prepared them for new jobs and roles both in Britain and America.

The market for print steadily expanded throughout the eighteenth-century Atlantic world thanks to printers' efforts to ensure that ordinary people knew how to read and use printed matter. Reading is and was a collection of practices, performed in diverse but always very specific ways. These practices were spread down the social hierarchy through printed guides. Eve Tavor Bannet explores guides to six manners or methods of reading, each with its own social, economic, commercial, intellectual and pedagogical functions, and each promoting a variety of fragmentary and discontinuous reading practices. The increasingly widespread production of periodicals, pamphlets, prefaces, conduct books, conversation-pieces and fictions, together with schoolbooks designed for adults and children, disseminated all that people of all ages and ranks might need or wish to know about reading, and prepared them for new jobs and roles both in Britain and America.