A mixed finite element method for the biharmonic equation. (English) Zbl 0632.65112

Monk, Peter

SIAM J. Numer. Anal. 24, 737-749 (1987).

The author applies mixed finite element techniques for solving the biharmonic equation on an arbitrary smooth plane domain under either clamped or simply supported boundary conditions. The approximations are based on the construction of particular finite-dimensional spaces in the standard Sobolev space of the first order and the Ritz-Galerkin method. A theorem about duality estimates for a general abstract problem is proved if a new hypothesis holds. By means of this result error estimates in the cases of clamped and simply-supported problems are obtained.

Reviewer: S.Gocheva-Ilieva

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
74S05	Finite element methods applied to problems in solid mechanics
31A30	Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J40	Boundary value problems for higher-order elliptic equations
74K20	Plates
65E05	General theory of numerical methods in complex analysis (potential theory, etc.)

Keywords:

mixed finite element techniques; biharmonic equation; Sobolev space; Ritz-Galerkin method; duality estimates; error estimates