Finite element methods for elliptic equations using nonconforming elements

Baker, Garth A.

doi:10.1090/S0025-5718-1977-0431742-5

Finite element methods for elliptic equations using nonconforming elements

Author: Garth A. Baker
Journal: Math. Comp. 31 (1977), 45-59
MSC: Primary 65N30
DOI: https://doi.org/10.1090/S0025-5718-1977-0431742-5
MathSciNet review: 0431742
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Abstract: A finite element method is developed for approximating the solution of the Dirichlet problem for the biharmonic operator, as a canonical example of a higher order elliptic boundary value problem.

The solution is approximated by special choices of classes of discontinuous functions, piecewise polynomial functions, by virtue of a special variational formulation of the boundary value problem. The approximating functions are not required to satisfy the prescribed boundary conditions.

Optimal error estimates are derived in Sobolev spaces.

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