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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.


On the Training/Test Distributions Gap: A Data Representation Learning Framework

Ben-David Shai

in Dataset Shift in Machine Learning

Published in print:
2008
Published Online:
August 2013
ISBN:
9780262170055
eISBN:
9780262255103
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262170055.003.0005
Subject:
Computer Science, Machine Learning

This chapter discusses some dataset shift learning problems from a formal, statistical point of view. It provides definitions for “multitask learning,” “inductive transfer,” and “domain adaptation,” ... More


The Stokes equations

A. M. Stuart and E. Söli

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/9780199678792.003.0004
Subject:
Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This chapter concerns the statement of the Stokes equations, a model of incompressible flows. It presents the weak formulation. This is followed by a description of finite element discretization and ... 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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