@article{1436028,
      recid = {1436028},
      author = {Ern, Alexandre, and Guermond, Jean-Luc,},
      title = {Finite elements., II,: Galerkin approximation, elliptic  and mixed PDEs /},
      pages = {1 online resource (ix, 492 pages) :},
      abstract = {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.},
      url = {http://library.usi.edu/record/1436028},
      doi = {https://doi.org/10.1007/978-3-030-56923-5},
}