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 | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0025-5718-1977-0431742-5
Article copyright:
© Copyright 1977
American Mathematical Society