000			02127nam a2200193Ia 4500
008			240821s9999 xx 000 0 und d
020			_a9783030563400 _qhbk
041			_aeng
082			_a620.001518 _bERN
100			_aErn, Alexandre
245		0	_aFinite Elements I Approximation and Interpolation _c/ Alexandre Ern and Jean-Luc Guermond
260			_bSpringer Nature _c2021 _aSwitzerland
300			_axii, 325 p. _c; 24 cm.
504			_aBib and Ref
520			_aThis book is the first 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 I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
650			_aDifferential equations, Partial Numerical solutions
700			_aGuermond, Jean-Luc
942			_cENGLISH
999			_c524090 _d524090