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NUMERICAL APPROXIMATION OF ONE-FLUID PROBLEMS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter addresses the discretization of the one-fluid magnetohydrodynamics equations. At the numerical level, the difficulties due to nonlinearities (coming both from the hydrodynamics equations ... More


Topics Concerning Finite Elements

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0008
Subject:
Mathematics, Numerical Analysis

Besides the first family of edge elements discussed in Chapter 5, there is a second family of elements of full polynomial degree at each order, also due to Nedelec. These have the potential advantage ... More


An Introduction to Nonlinear Finite Element Analysis

J. N. Reddy

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of ... More


The Finite Element Method: A Review

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/9780198525295.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic steps involved in the development of the finite element method as applied to one- and two-dimensional problems described by typical second-order differential equations. ... More


Flows of Viscous Incompressible Fluids

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/9780198525295.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Fluid mechanics is concerned with the motion of gases and liquids and their interaction with the surroundings. A fluid can either be inviscid (the viscosity is assumed to be zero) or incompressible ... More


Application of Weighted Residual Methods to Dynamic Economic Models

Ellen R. McGrattan

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:
10.1093/0199248273.003.0006
Subject:
Economics and Finance, Macro- and Monetary Economics

Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value ... More


INTRODUCTION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0001
Subject:
Mathematics, Numerical Analysis

This chapter presents reduced models of the compressible and incompressible Navier-Stokes equations which are used in the various discretization concepts discussed in the rest of the book. The ... More


Nonlinear Bending of Elastic Plates and Shells

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/9780198525295.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Simple two-dimensional plate and shell theories can be developed to study the deformation and stresses in plate structures undergoing small strains, small to moderate rotations, and large ... More


Mixed Multiscale Finite Element Methods on Adaptive Unstructured Grids Using Limited Global Information

J. E. Aarnes, Y. Efendiev, T.Y. Hou, and L. Jiang

in Multiscale Methods: Bridging the Scales in Science and Engineering

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199233854
eISBN:
9780191715532
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233854.003.0001
Subject:
Mathematics, Applied Mathematics

We study mixed multiscale finite element methods (MsFEM) on unstructured coarse grids. Unstructured grids are often used when highly heterogeneous reservoirs are discretized via irregular anisotropic ... More


Finite Element Formulations of Solid Continua

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/9780198525295.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the linear description of the motion of solid bodies, the displacements and strains are assumed to be very small and the material is linearly elastic. In addition, the equilibrium equations are ... More


Coarse-Grained Molecular Dynamics: Concurrent Multiscale Simulation at Finite Temperature Protect 1

Robert E. Rudd

in Multiscale Methods: Bridging the Scales in Science and Engineering

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199233854
eISBN:
9780191715532
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233854.003.0005
Subject:
Mathematics, Applied Mathematics

Coarse-grained molecular dynamics (CGMD) is a computer modeling technique that couples conventional molecular dynamics (MD) in some spatial regions of the simulation to a more coarse-grained ... More


Nonlinear Analysis of Time-Dependent Problems

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/9780198525295.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter, finite element models are used to solve time-dependent problems with nonlinearities and some standard time approximation schemes are described. All classes of nonlinear problems ... More


Some numerical methods for fluids

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199546909
eISBN:
9780191720482
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546909.003.0004
Subject:
Mathematics, Mathematical Physics

This chapter deals with the numerical methods that will be used for the flow solvers. As in most commercial and industrial packages, unstructured meshes with automatic mesh generation and adaptation ... 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


Nonlinear Bending of Straight Beams

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/9780198525295.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the application of the finite element method to the analysis of a slightly more complicated one-dimensional nonlinear problem: the bending of straight beams. When the applied ... More


Material Nonlinearities and Coupled Problems

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/9780198525295.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinearities arise from two independent sources: nonlinearity due to changes in the geometry or position of the material particles of a continuum, which is called the geometric nonlinearity, and ... More


A Posteriori Error Estimation Techniques for Finite Element Methods

Rüdiger Verfürth

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.001.0001
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

Self-adaptive discretization methods nowadays are an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to ... More


Introduction

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/9780198525295.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, ... More


Finite Element Formulations of Solid Continua

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the nonlinear continuum finite element formulation of elastic solids and presents updated and total Lagrangian finite element formulations using the principle of virtual ... More


Heat Transfer and Other Field Problems in Two Dimensions

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/9780198525295.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the use of the finite element method in analysing problems in which the coefficients of the differential equation are possibly functions of the dependent variable and its ... More


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