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Nonconforming finite element methods

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonconforming FEMs avoid the strong restrictions of conforming FEMs. So discontinuous ansatz and test functions, approximate test integrals, and strong forms are admitted. This allows the proof of ... More


Isochronous Systems

Francesco Calogero

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ... More


Evolution equations of the p-Laplacian type

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter presents the application of the foregoing ideas to the p-Laplacian evolution equation and the doubly nonlinear evolution equation. Topics covered include the doubly linear diffusion ... More


Introduction

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0001
Subject:
Mathematics, Applied Mathematics

This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about ... More


Heat Transfer and Other Field Problems in One Dimension

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the use of the finite element method in analysing heat transfer and other field problems in one dimension. A model nonlinear differential equation governing one-dimensional ... More


Finite‐Difference Methods for Continuous‐Time Dynamic Programming

Graham V. Candler

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0008
Subject:
Economics and Finance, Macro- and Monetary Economics

Introduces some of the methods and underlying ideas behind computational fluid dynamics—in particular, the use is discussed of finite‐difference methods for the simulation of dynamic economies. A ... More


LOGARITHMIC REDUCTION AND CYCLIC REDUCTION

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter is concerned with quadratically convergent algorithms for solving nonlinear matrix equations encountered in M/G/1, G/M/1, and QBD processes. The algorithm of logarithmic reduction for ... More


FUNCTIONAL ITERATIONS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0006
Subject:
Mathematics, Numerical Analysis

The major iterative algorithms based on functional iteration techniques for solving nonlinear matrix equations are described, analysed, and compared in this chapter. First, the basic concepts on ... More


Quantum Master Equations

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.03
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the fundamentals of the description of the quantum dynamics of open systems in terms of quantum master equations, together with its most important applications. Special ... More


Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations

Emery D. Conrad and John J. Tyson

in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262195485
eISBN:
9780262257060
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262195485.003.0006
Subject:
Mathematics, Mathematical Biology

This chapter explains how cell biologists can make reliable connections between molecular interaction networks and cell behaviors, when intuition fails in all but the simplest cases. It proposes to ... More


Resonant Wave Interactions and Resonant Excitation of Wave-guide Modes

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0012
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The idea of resonant nonlinear interactions of waves, and of resonant wave triads, is first explained using the example of Rossby waves, and then used to highlight a mechanism of excitation of ... More


The Energy Critical Wave Equation in 3D

Carlos Kenig

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0009
Subject:
Mathematics, Numerical Analysis

This chapter discusses the energy critical nonlinear wave equation in 3 space dimensions. It mainly focuses on soliton resolution for radial solutions of nonlinear waves. For a long time there has ... More


Parabolic Equations

Rüdiger Verfürth

in A Posteriori Error Estimation Techniques for Finite Element Methods

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.003.0006
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

We derive a posteriori error estimates for space–time finite element and certain finite volume discretisations of linear and nonlinear parabolic equations of second order. The starting point of our ... More


Nonlinear dynamics and chaos

Joseph F. Boudreau and Eric S. Swanson

in Applied Computational Physics

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198708636
eISBN:
9780191858598
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198708636.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Simple maps and dynamical systems are used to explore chaos in nature. The discussion starts with a review of the properties of nonlinear ordinary differential equations, including the useful ... More


Continuous-Valued Cellular Automata in Two Dimensions

Rudy Rucker

in New Constructions in Cellular Automata

Published in print:
2003
Published Online:
November 2020
ISBN:
9780195137170
eISBN:
9780197561652
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/9780195137170.003.0016
Subject:
Computer Science, Systems Analysis and Design

We explore a variety of two-dimensional continuous-valued cellular automata (CAs). We discuss how to derive CA schemes from differential equations and look at CAs based on several kinds of ... More


Bose Gas in One Dimension: Lieb–Liniger Model

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The coordinate Bethe ansatz can be extended to a model, the Lieb–Liniger model, of a one-dimensional gas of Bosons interacting with repulsive δ‎-function potentials. It has attracted attention due to ... More


Delay-Adaptive Linear Control

Yang Zhu and Miroslav Krstic

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202549
eISBN:
9780691203317
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202549.001.0001
Subject:
Mathematics, Applied Mathematics

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor ... More


Integrable Models

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0009
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a ... More


Weather by the Numbers: The Genesis of Modern Meteorology

Kristine C. Harper

Published in print:
2008
Published Online:
August 2013
ISBN:
9780262083782
eISBN:
9780262274982
Item type:
book
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262083782.001.0001
Subject:
Society and Culture, Technology and Society

For much of the first half of the twentieth century, meteorology was more art than science, dependent on an individual forecaster’s lifetime of local experience. This book tells the story of the ... More


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