Finite elements I : approximation and interpolation

Includes bibliographical references and index.

Part I: Elements of Functional Analysis. Lebesgue spaces ; Weak derivatives and Sobolev spaces ; Traces and Poincare 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.