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A mixed-Lagrange multiplier finite element method for the polyharmonic equation. (English) Zbl 0591.65073
The mixed method technique is applied for the approximation of the first boundary value problem for the polyharmonic equation. The problem is reformulated as a lower order system of equations so that a conforming finite element method can be used with only continuous finite elements. The linear system of equations resulting from the Galerkin method applied to the reformulated problem is easily preconditioned and efficiently solved by the conjugate gradient method.
Appropriate Lagrange multipliers are introduced so that the iteration scheme produced involves only a sequence of second order boundary problems with natural boundary conditions.
Reviewer: N.F.F.Ebecken

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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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