Higher order approximations to the boundary conditions for the finite element method

Blair, J. J.

doi:10.1090/S0025-5718-1976-0398123-3

Higher order approximations to the boundary conditions for the finite element method
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Math. Comp. 30 (1976), 250-262 Request permission

Abstract:

We consider here the approximation of essential boundary conditions for the finite element solutions of second order elliptic equations in two dimensions. Nonhomogeneous boundary conditions on curved boundaries are treated. The approach is to use trial functions which interpolate (in a generalized sense) functions satisfying the boundary conditions. The work is directed to showing in what manner this interpolation should be done to achieve the maximum accuracy and computational simplicity. These methods can be used to construct approximations of arbitrary high order of accuracy. Several examples are given.

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