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Finite Elements I = Approximation and Interpolation /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Finite Elements I/ by Alexandre Ern, Jean-Luc Guermond.
其他題名:	Approximation and Interpolation /
作者:	Ern, Alexandre.
其他作者:	Guermond, Jean-Luc.
面頁冊數:	XII, 325 p. 90 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Functional Analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-56341-7
ISBN:	9783030563417

Finite Elements I = Approximation and Interpolation /
Ern, Alexandre.

Finite Elements IApproximation and Interpolation /[electronic resource] :by Alexandre Ern, Jean-Luc Guermond. - 1st ed. 2021. - XII, 325 p. 90 illus.online resource. - Texts in Applied Mathematics,722196-9949 ;. - Texts in Applied Mathematics,59.

Part I: Elements of Functional Analysis -- Lebesgue spaces -- Weak derivatives and Sobolev spaces -- Traces and Poincaré Inequalities -- Duality in Sobolev spaces -- Part II: Introduction to Finite Elements -- Main ideas and definitions -- One-dimensional finite elements and tensorization -- Simplicial finite elements -- Part III: Finite element interpolation -- Meshes -- Finite element generation -- Mesh orientation -- Local interpolation on affine meshes -- Local inverse and functional inequalities -- Local interpolation on non-affine meshes -- H(div) finite elements -- H(curl) finite elements -- Local interpolation in H(div) and H(curl) (I) -- Local interpolation in H(div) and H(curl) (II) -- Part IV: Finite element spaces -- From broken to conforming spaces -- Main properties of the conforming spaces -- Face gluing -- Construction of the connectivity classes -- Quasi-interpolation and best approximation -- Commuting quasi-interpolation -- Appendices -- Banach and Hillbert spaces -- Differential calculus.

This 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.

ISBN: 9783030563417

Standard No.: 10.1007/978-3-030-56341-7doiSubjects--Topical Terms:

672166
Functional Analysis.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

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