Analysis of discretizations by the concept of discrete regularity. (English) Zbl 0531.65053

Hackbusch, W.

The mathematics of finite elements and applications IV, MAFELAP 1981, Proc. Conf., Uxbridge/Middlesex 1981, 369-376 (1982).

[For the entire collection see Zbl 0496.00017.]
The paper describes results obtained in a few recent publications of the author. These results are connected with the concept of discrete regularity usually used for finite difference methods. The author shows that this notion can be an essential tool in investigating some problems of the finite element methods as well. Problems of super-convergence and numerical integration in finite element methods are discussed as examples. Theorems on convergence for some nonlinear problems are formulated.

Reviewer: E.D’jakonov

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

discrete regularity; finite element methods; super-convergence

Citations:

Zbl 0496.00017