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001435390 019__ $$a1244623961$$a1246551926
001435390 020__ $$a9783030573485$$q(electronic bk.)
001435390 020__ $$a3030573486$$q(electronic bk.)
001435390 020__ $$z3030573478
001435390 020__ $$z9783030573478
001435390 0247_ $$a10.1007/978-3-030-57348-5$$2doi
001435390 035__ $$aSP(OCoLC)1244535657
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001435390 049__ $$aISEA
001435390 050_4 $$aQA377
001435390 08204 $$a515/.353$$223
001435390 1001_ $$aErn, Alexandre,$$d1967-
001435390 24510 $$aFinite elements.$$nIII,$$pFirst-order and time-dependent PDEs /$$cAlexandre Ern, Jean-Luc Guermond.
001435390 24630 $$aFirst-order and time-dependent PDEs
001435390 260__ $$aCham :$$bSpringer,$$c2021.
001435390 300__ $$a1 online resource
001435390 336__ $$atext$$btxt$$2rdacontent
001435390 337__ $$acomputer$$bc$$2rdamedia
001435390 338__ $$aonline resource$$bcr$$2rdacarrier
001435390 4901_ $$aTexts in Applied Mathematics Ser. ;$$vv. 74
001435390 504__ $$aIncludes bibliographical references and index.
001435390 5050_ $$aIntro -- Contents -- Part XII First-order PDEs -- 56 Friedrichs' systems -- 56.1 Basic ideas -- 56.1.1 The fields mathcalK and mathcalAk -- 56.1.2 Integration by parts -- 56.1.3 The model problem -- 56.2 Examples -- 56.2.1 Advection-reaction equation -- 56.2.2 Darcy's equations -- 56.2.3 Maxwell's equations -- 56.3 Weak formulation and well-posedness -- 56.3.1 Minimal domain, maximal domain, and graph space -- 56.3.2 The boundary operators N and M -- 56.3.3 Well-posedness -- 56.3.4 Examples -- 57 Residual-based stabilization -- 57.1 Model problem -- 57.2 Least-squares (LS) approximation
001435390 5058_ $$a57.2.1 Weak problem -- 57.2.2 Finite element setting -- 57.2.3 Error analysis -- 57.3 Galerkin/least-squares (GaLS) -- 57.3.1 Local mesh-dependent weights -- 57.3.2 Discrete problem and error analysis -- 57.3.3 Scaling -- 57.3.4 Examples -- 57.4 Boundary penalty for Friedrichs' systems -- 57.4.1 Model problem -- 57.4.2 Boundary penalty method -- 57.4.3 GaLS stabilization with boundary penalty -- 58 Fluctuation-based stabilization (I) -- 58.1 Discrete setting -- 58.2 Stability analysis -- 58.3 Continuous interior penalty -- 58.3.1 Design of the CIP stabilization -- 58.3.2 Error analysis
001435390 5058_ $$a58.4 Examples -- 59 Fluctuation-based stabilization (II) -- 59.1 Two-scale decomposition -- 59.2 Local projection stabilization -- 59.3 Subgrid viscosity -- 59.4 Error analysis -- 59.5 Examples -- 60 Discontinuous Galerkin -- 60.1 Discrete setting -- 60.2 Centered fluxes -- 60.2.1 Local and global formulation -- 60.2.2 Error analysis -- 60.2.3 Examples -- 60.3 Tightened stability by jump penalty -- 60.3.1 Local and global formulation -- 60.3.2 Error analysis -- 60.3.3 Examples -- 61 Advection-diffusion -- 61.1 Model problem -- 61.2 Discrete setting -- 61.3 Stability and error analysis
001435390 5058_ $$a61.3.1 Stability and well-posedness -- 61.3.2 Consistency/boundedness -- 61.3.3 Error estimates -- 61.4 Divergence-free advection -- 62 Stokes equations: Residual-based stabilization -- 62.1 Model problem -- 62.2 Discrete setting for GaLS stabilization -- 62.3 Stability and well-posedness -- 62.4 Error analysis -- 63 Stokes equations: Other stabilizations -- 63.1 Continuous interior penalty -- 63.1.1 Discrete setting -- 63.1.2 Stability and well-posedness -- 63.1.3 Error analysis -- 63.2 Discontinuous Galerkin -- 63.2.1 Discrete setting -- 63.2.2 Stability and well-posedness
001435390 5058_ $$a63.2.3 Error analysis -- Part XIII Parabolic PDEs -- 64 Bochner integration -- 64.1 Bochner integral -- 64.1.1 Strong measurability and Bochner integrability -- 64.1.2 Main properties -- 64.2 Weak time derivative -- 64.2.1 Strong and weak time derivatives -- 64.2.2 Functional spaces with weak time derivative -- 65 Weak formulation and well-posedness -- 65.1 Weak formulation -- 65.1.1 Heuristic argument for the heat equation -- 65.1.2 Abstract parabolic problem -- 65.1.3 Weak formulation -- 65.1.4 Example: the heat equation -- 65.1.5 Ultraweak formulation -- 65.2 Well-posedness
001435390 506__ $$aAccess limited to authorized users.
001435390 520__ $$aThis book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.
001435390 650_0 $$aDifferential equations, Partial.
001435390 650_0 $$aFinite element method.
001435390 650_6 $$aÉquations aux dérivées partielles.
001435390 650_6 $$aMéthode des éléments finis.
001435390 655_0 $$aElectronic books.
001435390 7001_ $$aGuermond, Jean-Luc.
001435390 77608 $$iPrint version:$$aErn, Alexandre, 1967-$$tFinite elements. III, First-order and time-dependent PDEs.$$dCham : Springer, 2021$$z3030573478$$z9783030573478$$w(OCoLC)1176317798
001435390 830_0 $$aTexts in applied mathematics ;$$v74.
001435390 852__ $$bebk
001435390 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-57348-5$$zOnline Access$$91397441.1
001435390 909CO $$ooai:library.usi.edu:1435390$$pGLOBAL_SET
001435390 980__ $$aBIB
001435390 980__ $$aEBOOK
001435390 982__ $$aEbook
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