000			02414nam a2200217Ia 4500
008			240821s9999 xx 000 0 und d
020			_a9783030569228 _qhbk
041			_aeng
082			_a620.001518 _bERN
100			_aErn, Alexandre
245		0	_aFinite Elements Ii Galerkin Approximation Elliptic and Mixed Pdes _c/ Alexandre Ern and Jean-Lue Guermond
260			_bSpringer _c2021 _aCham, Switzerland
300			_aix, 492 p. _b: ill. (some col.) _c; 24 cm.
504			_aBib and Ref
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. .
650			_aEngineering
650			_aFunctional analysis
650			_aFinite element method
700			_aGuermond, Jean-Lue
942			_cENGLISH
999			_c524091 _d524091