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Hierarchical bases and the finite element method. (English) Zbl 0865.65078
Iserles, A. (ed.), Acta Numerica Vol. 5, 1996. Cambridge: Cambridge University Press. 1-43 (1996).
This paper presents a brief introduction to hierarchical bases and the important part they play in contemporary finite element calculations. In particular, their role in a posteriori error estimation is examined together with their role in the formulation of iterative methods for solving large sparse sets of linear equations arising from finite element discretization. Some topics discussed are: two-level iterative methods, multi-level Cauchy inequalities, and multi-level iterative methods.
For the entire collection see [Zbl 0845.00011].

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65F50 Computational methods for sparse matrices
65F10 Iterative numerical methods for linear systems