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## Finite Element Methods for Maxwell's Equations

*Peter Monk*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.001.0001
- Subject:
- Mathematics, Numerical Analysis

Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and ... More

## Local Error Estimate and Variable Stepsize

*Alfredo Bellen and Marino Zennaro*

### in Numerical Methods for Delay Differential Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506546
- eISBN:
- 9780191709609
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506546.003.0007
- Subject:
- Mathematics, Numerical Analysis

This chapter focuses on the stepsize control mechanism, which plays a central role in the production of efficient numerical codes for DDEs. In particular, the importance of the choice of the ... More

## Finite Elements Methods for the Cavity Problem

*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/9780198508885.003.0007
- Subject:
- Mathematics, Numerical Analysis

This chapter concerns the use of edge finite element methods to approximate the cavity problem with mixed boundary data. It provides two proofs of convergence of the discrete solution. First under ... More

## Finite Elements on Tetrahedra

*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/9780198508885.003.0005
- Subject:
- Mathematics, Numerical Analysis

The finite element method is based on a geometric decomposition of the domain of Maxwell’s equations into simple elements. This chapter is devoted to tetrahedral elements, which are very common in ... More

## FUNDAMENTAL CONCEPTS IN ONE DIMENSION

*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/9780198528692.003.0002
- Subject:
- Mathematics, Numerical Analysis

This chapter discusses the fundamental concepts that are further developed in the remainder of the book, in the context of a one-dimensional formulation. In doing so, the principles and underlying ... More

## Scattering by a Bounded Inhomogeneity

*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/9780198508885.003.0011
- Subject:
- Mathematics, Numerical Analysis

This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the ... More

## The Scattering Problem Using Calderon Maps

*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/9780198508885.003.0010
- Subject:
- Mathematics, Numerical Analysis

This chapter presents a finite element method for scattering by a bounded scatterer in an infinite homogeneous background. The first task is to reduce the problem to a bounded domain, and in this ... More

## Finite Elements on Hexahedra

*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/9780198508885.003.0006
- Subject:
- Mathematics, Numerical Analysis

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several ... More

## Measuring Uncertainty and Error Directly from End Estimates

*Andrea Volkens, Judith Bara, Ian Budge, Michael D. McDonald, Robin Best, and Simon Franzmann*

### in Mapping Policy Preferences From Texts: Statistical Solutions for Manifesto Analysts

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199640041
- eISBN:
- 9780191757181
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199640041.003.0007
- Subject:
- Political Science, Comparative Politics

This chapter starts by re-emphasising the importance of context in assessing estimate uncertainty and error. This not only means bringing general validity and reliability to the assessment but also ... More

## Business Forecasting and Credit Decisions

*Hrishikes Bhattacharya*

### in Banking Strategy, Credit Appraisal, and Lending Decisions: A Risk–Return Framework

- Published in print:
- 2011
- Published Online:
- September 2012
- ISBN:
- 9780198074106
- eISBN:
- 9780199080861
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198074106.003.0013
- Subject:
- Economics and Finance, Financial Economics

This chapter discusses one of the most reliable and commonly used techniques of business forecasting, and develops an appraisal methodology by applying this technique. Of the various statistical ... More

## Advantages of Cognitive Limitations

*Yaakov Kareev*

### in Evolution and the Mechanisms of Decision Making

- Published in print:
- 2012
- Published Online:
- May 2016
- ISBN:
- 9780262018081
- eISBN:
- 9780262306027
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262018081.003.0010
- Subject:
- Psychology, Social Psychology

Being a product of evolutionary pressures, it would not be surprising to find that what seems to be a limitation of the cognitive system is actually a fine-tuned compromise between a set of competing ... More

## Metric-Based Approaches for Semi-Supervised Regression and Classification

*Schuurmans Dale, Southey Finnegan, Wilkinson Dana, and Guo Yuhong*

### in Semi-Supervised Learning

- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262033589
- eISBN:
- 9780262255899
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262033589.003.0023
- Subject:
- Computer Science, Machine Learning

This chapter discusses the explicit relationship that must be asserted between labeled and unlabeled data, which is a requirement of semi-supervised learning methods. Semi-supervised model selection ... More

## Explicit Error Bounds via Total Variation

*Lutz Dümbgen and Christoph Leuenberger*

### in Benford's Law: Theory and Applications

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691147611
- eISBN:
- 9781400866595
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147611.003.0005
- Subject:
- Mathematics, Probability / Statistics

This chapter concerns the obtaining of explicit error estimates for convergence to Benford's law, with an analysis done through the total variation of the densities. This method yields reasonable ... More

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