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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Finite element methods for elliptic equations using nonconforming elements


Author: Garth A. Baker
Journal: Math. Comp. 31 (1977), 45-59
MSC: Primary 65N30
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1977-0431742-5
PII: S 0025-5718(1977)0431742-5
Article copyright: © Copyright 1977 American Mathematical Society