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## Numerical Method

*Gary A. Glatzmaier*

### in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. ... More

## Ionic soft matter

*Masao Doi*

### in Soft Matter Physics

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199652952
- eISBN:
- 9780191774942
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652952.003.0010
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Ionic soft matter includes suspensions of charged colloidal particles, polyelectrolyte solutions, polyelectrolyte gels, ionic micelles, etc. A common special feature in these materials is that they ... 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

## The Poisson Equation

*Howard C. Elman, David J. Silvester, and Andrew J. Wathen*

### in Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199678792
- eISBN:
- 9780191780745
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199678792.003.0002
- Subject:
- Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This chapter concerns the statement of the Poisson equation and its weak formulation. This is followed by a description of finite element discretization and properties of the discrete problem.

## The evolution of the large-scale structure of the universe: beyond the linear regime

*Francis Bernardeau*

### in Post-Planck Cosmology: Lecture Notes of the Les Houches Summer School: Volume 100, July 2013

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198728856
- eISBN:
- 9780191795794
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198728856.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces analytical tools, methods, and results describing the growth of large-scale structure beyond the linear regime. The presentation focuses on the single-flow regime of the ... More

## Finite Difference Methods

*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/9780198805021.003.0014
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by ... More

## Essentials of Electricity and Magnetism

*Richard Freeman, James King, and Gregory Lafyatis*

### in Electromagnetic Radiation

- Published in print:
- 2019
- Published Online:
- February 2019
- ISBN:
- 9780198726500
- eISBN:
- 9780191793325
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198726500.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to ... More

## Two-Dimensional Problems Involving a Single Variable

*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/9780199641758.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter presents the weak-form Galerkin finite element model of a generalized, nonlinear Poisson equation in two-dimensions for both steady-state and transient response. It discusses the ... More

## The electrostatics of conductors

*J. Pierrus*

### in Solved Problems in Classical Electromagnetism: Analytical and Numerical Solutions with Comments

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198821915
- eISBN:
- 9780191861055
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821915.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter begins by proving some important properties of (i) conductors in electrostatic equilibrium, and (ii) harmonic functions. These results underpin most of the remaining questions of Chapter ... More

## Fourier Integral and Sobolev Space Hs

*Fon-Che Liu*

### in Real Analysis

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198790426
- eISBN:
- 9780191831676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198790426.003.0007
- Subject:
- Mathematics, Analysis

The Fourier integral, which is often called a Fourier transform, is based on an idea of J. Fourier for resolving functions into basic harmonics in the treatment of heat conduction. The Fourier ... More

## The law of gravitation

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0011
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter embarks on the study of Newton’s law of gravitation. It first discusses gravitational mass and inertial mass, a measure of the ‘resistance’ of the point particle to an applied force. The ... More

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