The mathematical theory of finite element methods / Susanne C. Brenner, L. Ridgeway Scott.

• Basic Concepts -- Sobolev Spaces -- Variational Formulation of Elliptic Boundary Value Problems -- The Construction of a Finite Element Space -- Polynomial Approximation Theory in Sobolev Spaces -- n-Dimensional Variational Problems -- Finite Element Multigrid Methods -- Additive Schwarz Preconditioners -- Max—norm Estimates -- Adaptive Meshes -- Variational Crimes -- Applications to Planar Elasticity -- Mixed Methods -- Iterative Techniques for Mixed Methods -- Applications of Operator-Interpolation Theory. 

• This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincaré-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout. The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. 

Ämnesord

Diskret matematik  (sao)

Boundary value problems  -- Numerical solutions (LCSH)

Finite element method  -- Mathematics (LCSH)

Klassifikation

515.35 (DDC)

518.25 (DDC)

65N30 (msc)

65-01 (msc)

46N40 (msc)

65M60 (msc)

74S05 (msc)

Tdcbb (kssb/8 (machine generated))