Finite elements I : approximation and interpolation
Ern, Alexandre
Finite elements I : approximation and interpolation by Alexandre Ern and Jean-Luc Guermond. - Switzerland : Springer, ©2021 - xii, 325 p. : ill. ; 24 cm. - Texts in Applied Mathematics ; Volume 75 .
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.
9783030563400
Finite element method.
Differential equations, Partial -- Numerical solutions.
Finite element method.
515.353 / ERN-F
Finite elements I : approximation and interpolation by Alexandre Ern and Jean-Luc Guermond. - Switzerland : Springer, ©2021 - xii, 325 p. : ill. ; 24 cm. - Texts in Applied Mathematics ; Volume 75 .
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.
9783030563400
Finite element method.
Differential equations, Partial -- Numerical solutions.
Finite element method.
515.353 / ERN-F