02455nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245015500252260008200407300003400489336002600523337002600549338003600575347002400611490004000635506006600675520099000741650003501731650004001766650006601806650002801872650004001900700003201940856003201972856006502004253-200706CH-001817-320200706233004.0a fot ||| 0|cr nn mmmmamaa200706e20200806sz fot ||| 0|eng d a978303719706670a10.4171/2062doi ach0018173 7aPBKJ2bicssc a35-xxa49-xxa65-xxa74-xx2msc1 aRepin, Sergey I.,eauthor.10aAccuracy of Mathematical Modelsh[electronic resource] :bDimension Reduction, Homogenization, and Simplification /cSergey I. Repin, Stefan A. Sauter3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2020 a1 online resource (333 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v331 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 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.07aDifferential equations2bicssc07aPartial differential equations2msc07aCalculus of variations and optimal control; optimization2msc07aNumerical analysis2msc07aMechanics of deformable solids2msc1 aSauter, Stefan A.,eauthor.40uhttps://doi.org/10.4171/206423cover imageuhttps://www.ems-ph.org/img/books/repin_mini.jpg