| Dewey Class |
515 |
| Title |
Finite Elements II ([EBook] :) : Galerkin Approximation, Elliptic and Mixed PDEs / / by Alexandre Ern, Jean-Luc Guermond. |
| Author |
Ern, Alexandre |
| Added Personal Name |
Guermond, Jean-Luc |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2021. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2021. |
| Physical Details |
IX, 492 p. 28 illus., 1 illus. in color. : online resource. |
| Series |
Texts in applied mathematics 2196-9949 ; ; 73 |
| ISBN |
9783030569235 |
| Summary Note |
This 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.: |
| Contents note |
Part 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. |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-56923-5 |
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