Accuracy of Mathematical Models ; Dimension Reduction, Homogenization, and Simplification.

Format:

Book

Author/Creator:

Repin, Author.

Sauter, Stefan A., author.

Series:

EMS Tracts in Mathematics (etm) 2943-5005 33

Language:

English

Physical Description:

1 online resource (333 pages)

Place of Publication:

EMS Press 2020

Zuerich, Switzerland : European Mathematical Society Publishing House, 2020

Language Note:

English

System Details:

text file PDF

Summary:

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.

ISBN:

3-03719-706-4