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001436028 001__ 1436028
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001436028 019__ $$a1247670761$$a1247677346
001436028 020__ $$a9783030569235$$q(electronic bk.)
001436028 020__ $$a3030569233$$q(electronic bk.)
001436028 020__ $$z9783030569228$$q(print)
001436028 020__ $$z3030569225
001436028 0247_ $$a10.1007/978-3-030-56923-5$$2doi
001436028 035__ $$aSP(OCoLC)1247885582
001436028 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX$$dOCLCO$$dEBLCP$$dOCLCF$$dUKAHL$$dOCLCQ$$dCOM$$dOCLCO$$dSFB$$dOCLCQ
001436028 049__ $$aISEA
001436028 050_4 $$aQA377
001436028 08204 $$a518/.25$$223
001436028 1001_ $$aErn, Alexandre,$$d1967-$$eauthor.
001436028 24510 $$aFinite elements.$$nII,$$pGalerkin approximation, elliptic and mixed PDEs /$$cAlexandre Ern, Jean-Luc Guermond.
001436028 24630 $$aGalerkin approximation, elliptic and mixed PDEs
001436028 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2021]
001436028 300__ $$a1 online resource (ix, 492 pages) :$$billustrations (some color)
001436028 336__ $$atext$$btxt$$2rdacontent
001436028 337__ $$acomputer$$bc$$2rdamedia
001436028 338__ $$aonline resource$$bcr$$2rdacarrier
001436028 4901_ $$aTexts in applied mathematics,$$x0939-2475 ;$$vvolume 73
001436028 504__ $$aIncludes bibliographical references and index.
001436028 5050_ $$aPart V: Weak formulations and well-posedness -- Weak formulation of model problems -- Main results on well-posedness -- Part VI: Galerkin approximation -- Basic error analysis -- Error analysis with variational crimes -- Linear algebra -- Sparse matrices -- Quadratures -- Part VII: Elliptic PDEs: conforming approximation -- Scalar second-order elliptic PDEs -- H1-conforming approximation (I) -- H1-conforming approximation (II) -- A posteriori error analysis -- The Helmholtz problem -- Part VIII: Elliptic PDEs: nonconforming approximation -- Crouzeix-Raviart approximation -- Nitsche's boundary penalty method -- Discontinuous Galerkin -- Hybrid high-order methods -- Contrasted diffusivity (I) -- Contrasted diffusivity (II) -- Part IX: Vector-valued elliptic PDEs -- Linear elasticity -- Maxwell's equations: H(curl)-approximation -- Maxwell's equations: control on the divergence -- Maxwell's equations: further topics -- Part X: Eigenvalue problems -- Symmetric elliptic eigenvalue problems -- Symmetric operators, conforming approximation -- Nonsymmetric problems -- Part XI: PDEs in mixed form -- Well-posedness for PDEs in mixed form -- Mixed finite element approximation -- Darcy's equations -- Potential and flux recovery -- Stokes equations: Basic ideas -- Stokes equations: Stable Pairs (I) -- Stokes equations: Stable pairs (II) -- Appendices -- Bijective operators in Banach spaces.
001436028 506__ $$aAccess limited to authorized users.
001436028 520__ $$aThis book is the second 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 II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix--Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
001436028 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 27, 2021).
001436028 650_0 $$aFinite element method.
001436028 650_0 $$aDifferential equations, Partial$$xNumerical solutions.
001436028 650_0 $$aFunctional analysis.
001436028 650_0 $$aGalerkin methods.
001436028 650_6 $$aMéthode des éléments finis.
001436028 650_6 $$aÉquations aux dérivées partielles$$xSolutions numériques.
001436028 650_6 $$aAnalyse fonctionnelle.
001436028 650_6 $$aMéthode de Galerkin.
001436028 655_0 $$aElectronic books.
001436028 7001_ $$aGuermond, Jean-Luc,$$eauthor.
001436028 77608 $$iPrint version:$$aErn, Alexandre, 1967-$$tFinite elements. II, Galerkin approximation, elliptic and mixed PDEs.$$dCham, Switzerland : Springer, [2021]$$z3030569225$$z9783030569228$$w(OCoLC)1176323477
001436028 830_0 $$aTexts in applied mathematics ;$$v73.$$x0939-2475
001436028 852__ $$bebk
001436028 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-56923-5$$zOnline Access$$91397441.1
001436028 909CO $$ooai:library.usi.edu:1436028$$pGLOBAL_SET
001436028 980__ $$aBIB
001436028 980__ $$aEBOOK
001436028 982__ $$aEbook
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