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On the multi-level splitting of finite element spaces. (English) Zbl 0608.65065
This paper is concerned with the condition number of the discretization matrix when solving second order elliptic problems in the plane. It is shown that the condition number is much better for hierarchical bases than for the more common nodal bases. When a preconditioned conjugate gradient method is applied for the solution, this results in almost optimal operation counts, similarly as for multi-level methods. The results are demonstrated on some numerical examples.
Reviewer: H.Matthies

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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