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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


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


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


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


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


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


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


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


Krylov Subspace Methods

Jörg Liesen and Zdenek Strakos

in Krylov Subspace Methods: Principles and Analysis

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199655410
eISBN:
9780191744174
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655410.003.0002
Subject:
Mathematics, Applied Mathematics, Algebra

This chapter derives, under natural conditions and assumptions, the main ideas of Krylov subspace methods from a general projection framework. Incorporating the Krylov subspaces as search spaces in ... More


Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids

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/9780199641758.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents finite element models of flows of viscous incompressible fluids for Newtonian and non-Newtonian (power-law) fluids. It develops two different finite element models, namely, the ... 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


Least-Squares Finite Element Models of Flows of Viscous Incompressible Fluids

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/9780199641758.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops finite element formulations for flows of viscous incompressible fluids using high-order spectral/hp finite element technology and least-squares finite element formulation. The ... More


Nonlinear Elasticity, Plasticity, and Viscoelasticity

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/9780199641758.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses finite element models of materially nonlinear elastic and plastic models of one-dimensional problems. It presents efficient and accurate locking-free linear viscoelastic beam ... More


Continuum dynamics

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/9780198708636.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The theory and application of a variety of methods to solve partial differential equations are introduced in this chapter. These methods rely on representing continuous quantities with discrete ... 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


The Finite-Element Method—Part I

Shiro Kobayashi, Soo-Ik Oh, and Taylan Altan

in Metal Forming and the Finite-Element Method

Published in print:
1989
Published Online:
November 2020
ISBN:
9780195044027
eISBN:
9780197560006
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195044027.003.0009
Subject:
Chemistry, Materials Chemistry

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular ... More


Introduction to the finite element method for linear elastostatics

Lallit Anand and Sanjay Govindjee

in Continuum Mechanics of Solids

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198864721
eISBN:
9780191896767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198864721.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the widely-used finite element method applied to solving two-dimensional boundary value problems in linear elastostatics under plane strain or plane stress conditions. While ... More


General Introduction and Mathematical Preliminaries

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/9780199641758.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter explains the development of mathematical models and numerical evaluation of the mathematical models using the finite element method. It also discusses nonlinear analysis and some ... More


Computational Seismology: A Practical Introduction

Heiner Igel

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198717409
eISBN:
9780191835070
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198717409.001.0001
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This volume is an introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering, and many other fields. The physical problem ... More


Methods of Analysis

Shiro Kobayashi, Soo-Ik Oh, and Taylan Altan

in Metal Forming and the Finite-Element Method

Published in print:
1989
Published Online:
November 2020
ISBN:
9780195044027
eISBN:
9780197560006
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195044027.003.0008
Subject:
Chemistry, Materials Chemistry

In Chap. 4 we described fundamentals for the analysis of metal-forming processes and derived some useful principles.


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