Superconvergence in Galerkin finite element methods. (English) Zbl 0826.65092

Wahlbin, Lars B.

Lecture Notes in Mathematics. 1605. Berlin: Springer Verlag. xi, 166 p. (1995).

This book discusses superconvergence of Galerkin finite element methods applied to second-order elliptic problems with sufficiently smooth solutions. The results are sensitive to the choice of elements and test functions, and this book elaborates on their aspect of the problem in depth. The book includes an interesting brief chapter on nonlinear problems. It also discusses superconvergence of approximations to derivatives of the solution function.
The book originates from seminar notes, and is written in an informal and quite readable style. Numerous references to the extensive literature in this area are included.

Reviewer: Michael Sever (Jerusalem)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65-02	Research exposition (monographs, survey articles) pertaining to numerical analysis
35J25	Boundary value problems for second-order elliptic equations
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

monograph; Galerkin finite element methods; second-order elliptic problems; smooth solutions; nonlinear problems; superconvergence