## 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*

- 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*

- 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.