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001434396 001__ 1434396
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001434396 019__ $$a1238004955$$a1244117619$$a1249943568$$a1253408855
001434396 020__ $$a9783030563417$$q(electronic book)
001434396 020__ $$a3030563413$$q(electronic book)
001434396 020__ $$a9783030563424$$q(print)
001434396 020__ $$a3030563421
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001434396 020__ $$z9783030563400
001434396 0247_ $$a10.1007/978-3-030-56341-7$$2doi
001434396 035__ $$aSP(OCoLC)1239982700
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001434396 049__ $$aISEA
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001434396 08204 $$a518/.25$$223
001434396 1001_ $$aErn, Alexandre,$$d1967-$$eauthor.
001434396 24510 $$aFinite elements.$$nI,$$pApproximation and interpolation /$$cAlexandre Ern, Jean-Luc Guermond.
001434396 24630 $$aApproximation and interpolation
001434396 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2021]
001434396 300__ $$a1 online resource
001434396 336__ $$atext$$btxt$$2rdacontent
001434396 337__ $$acomputer$$bc$$2rdamedia
001434396 338__ $$aonline resource$$bcr$$2rdacarrier
001434396 347__ $$atext file
001434396 347__ $$bPDF
001434396 4901_ $$aTexts in applied mathematics ;$$vvolume 72
001434396 504__ $$aIncludes bibliographical references and index.
001434396 5050_ $$aPart I: Elements of Functional Analysis. Lebesgue spaces ; Weak derivatives and Sobolev spaces ; Traces and Poincare Inequalities ; Duality in Sobolev spaces -- Part II: Introduction to Finite Elements. Main ideas and definitions ; One-dimensional finite elements and tensorization ; Simplicial finite elements -- Part III: Finite element interpolation. Meshes ; Finite element generation ; Mesh orientation ; Local interpolation on affine meshes ; Local inverse and functional inequalities ; Local interpolation on non-affine meshes ; H(div) finite elements ; H(curl) finite elements ; Local interpolation in H(div) and H(curl) (I) ; Local interpolation in H(div) and H(curl) (II) -- Part IV: Finite element spaces. From broken to conforming spaces ; Main properties of the conforming spaces ; Face gluing ; Construction of the connectivity classes ; Quasi-interpolation and best approximation ; Commuting quasi-interpolation -- Appendices. Banach and Hillbert spaces ; Differential calculus.
001434396 506__ $$aAccess limited to authorized users.
001434396 520__ $$aThis book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
001434396 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 30, 2021).
001434396 650_0 $$aFinite element method.
001434396 650_0 $$aDifferential equations, Partial$$xNumerical solutions.
001434396 650_0 $$aFunctional analysis.
001434396 650_6 $$aMéthode des éléments finis.
001434396 650_6 $$aÉquations aux dérivées partielles$$xSolutions numériques.
001434396 650_6 $$aAnalyse fonctionnelle.
001434396 655_0 $$aElectronic books.
001434396 7001_ $$aGuermond, Jean-Luc,$$eauthor.
001434396 77608 $$iPrint version:$$z9783030563400
001434396 830_0 $$aTexts in applied mathematics ;$$v72.
001434396 852__ $$bebk
001434396 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-56341-7$$zOnline Access$$91397441.1
001434396 909CO $$ooai:library.usi.edu:1434396$$pGLOBAL_SET
001434396 980__ $$aBIB
001434396 980__ $$aEBOOK
001434396 982__ $$aEbook
001434396 983__ $$aOnline
001434396 994__ $$a92$$bISE