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Hierarchical conforming finite element methods for the biharmonic equation. (English) Zbl 0771.65071
The author investigates the structure of two finite element approximations for the biharmonic operator based on triangulations of the region and the use of hierarchical bases. He shows that for them it is possible to construct some nearly optimal preconditioners and thereby to use effective modifications of classical iterative methods.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J40 Boundary value problems for higher-order elliptic equations
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