LEADER 03724nam 22005655 450 001 9910254093303321 005 20200705070659.0 010 $a3-319-32354-7 024 7 $a10.1007/978-3-319-32354-1 035 $a(CKB)3710000000718284 035 $a(DE-He213)978-3-319-32354-1 035 $a(MiAaPQ)EBC6315000 035 $a(MiAaPQ)EBC5578353 035 $a(Au-PeEL)EBL5578353 035 $a(OCoLC)951669864 035 $a(PPN)194378950 035 $a(EXLCZ)993710000000718284 100 $a20160602d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Approximation of Partial Differential Equations /$fby Sören Bartels 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XV, 535 p. 170 illus.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v64 300 $aIncludes index. 311 $a3-319-32353-9 327 $aPreface -- Part I Finite differences and finite elements -- Elliptic partial differential equations -- Finite Element Method -- Part II Local resolution and iterative solution -- Local Resolution Techniques -- Iterative Solution Methods -- Part III Constrained and singularly perturbed problems -- Saddled-point Problems -- Mixed and Nonstandard methods -- Applications -- Problems and Projects -- Implementation aspects -- Notations, inequalities, guidelines -- Index . 330 $aFinite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods. 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v64 606 $aNumerical analysis 606 $aPartial differential equations 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aNumerical analysis. 615 0$aPartial differential equations. 615 14$aNumerical Analysis. 615 24$aPartial Differential Equations. 676 $a515.353 700 $aBartels$b Sören$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755547 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254093303321 996 $aNumerical approximation of partial differential equations$91523524 997 $aUNINA