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Incremental unknowns method and compact schemes. (English) Zbl 0914.65110
The aim of this paper is to establish a link between the compact scheme discretization techniques and the incremental unknowns method (IU) in the double context of hierarchical methods and nonlinear Galerkin methods. For this purpose on the one hand the author uses a compact scheme for defining high-order incremental unknowns, and on the other hand he uses the incremental unknowns for preconditioning the underlying matrices of high-order discretization of the elliptic problem.
Finally some numerical results are presented which are related a combination of the IU method and the compact scheme. The efficiency of the data compression method is illustrated and the decay of magnitude of the structures according to the grid level to which they belong is compared. After that Dirichlet problems are considered for which second-order IU is used for preconditioning the matrix and efficient high accurate solutions are obtained.
Reviewer: A.L.Pletea (Iaşi)

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
65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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