\(p\)- and \(hp\)-finite element methods. Theory and applications in solid and fluid mechanics. (English) Zbl 0910.73003

Schwab, Ch.

Numerical Mathematics and Scientific Computation. Oxford: Clarendon Press. xii, 374 p. (1998).

This book resulted from courses on finite element analysis taught by the author in 1989/96 in Zürich. As such, the text is intended as an up-to-date view of the mathematical techniques used to establish \(p\)- or spectral convergence results of higher order, and \(hp\)- and spectral element methods. The investigation of where and when such methods are recommended in preference to the more classical \(h\)-version of finite elements is carefully presented with emphasis on singularly perturbed problems.
The book is recommended to graduate mathematical students and engineers seeking a good reference text on the title problem.

Reviewer: J.C.F.Telles (Rio de Janeiro)

MSC:

74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
74S15	Boundary element methods applied to problems in solid mechanics
76M10	Finite element methods applied to problems in fluid mechanics
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis

Keywords:

higher-order elements; spectral elements; spectral convergence; singularly perturbed problems