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Accuracy of Mathematical Models
EMS Tracts in Mathematics Vol. 33

Sergey I. Repin (Russian Academy of Sciences, St. Petersburg, Russian Federation)
Stefan A. Sauter (Universität Zürich, Switzerland)

Accuracy of Mathematical Models

Dimension Reduction, Homogenization, and Simplification

ISBN print 978-3-03719-206-1, ISBN online 978-3-03719-706-6
DOI 10.4171/206
August 2020, 333 pages, hardcover, 17 x 24 cm.
59.00 Euro

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.

Keywords: Modelling error, a posteriori error majorant, model simplification, dimension reduction, homogenization, conversion of models

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