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An optimal order multigrid method for biharmonic, \(C^ 1\) finite element equations. (English) Zbl 0667.65089
We study a special multigrid method for solving large linear systems which arise from discretizing biharmonic problems by the Hsieh-Clough- Tocher, \(C^ 1\) macro finite elements or several other \(C^ 1\) finite elements. Since the multiple \(C^ 1\) finite element spaces considered are not nested, the nodal interpolation operator is used to transfer functions between consecutive levels in the multigrid method. This method converges with the optimal computational order.
Reviewer: S.Zhang

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