Header

UZH-Logo

Maintenance Infos

Accuracy of mathematical models: Dimension reduction, homogenization, and simplification


Repin, Sergey; Sauter, Stefan A (2020). Accuracy of mathematical models: Dimension reduction, homogenization, and simplification. Berlin, Switzerland: European Mathematical Society.

Abstract

The expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control.
This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates.

Abstract

The expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control.
This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates.

Statistics

Citations

Dimensions.ai Metrics

Altmetrics

Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Language:English
Date:31 July 2020
Deposited On:18 Dec 2020 13:15
Last Modified:18 Dec 2020 13:15
Publisher:European Mathematical Society
Series Name:EMS Tracts in Mathematics
Volume:33
Number of Pages:333
ISBN:978 3 03719 206 1
OA Status:Closed
Publisher DOI:https://doi.org/10.4171/206

Download

Full text not available from this repository.
View at publisher

Get full-text in a library