A Clough-Tocher type element useful for fourth order problems over nonpolygonal domains

Mansfield, Lois

doi:10.1090/S0025-5718-1978-0468241-1

A Clough-Tocher type element useful for fourth order problems over nonpolygonal domains
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Math. Comp. 32 (1978), 135-142 Request permission

Abstract:

A new macro-element useful for finite element approximations to fourth order elliptic problems with curved boundaries is presented. An error analysis is given which shows that these elements achieve $O({h^2})$ accuracy in energy.

References

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Conferences on Matrix Methods in Structural Mechanics

Lois Mansfield, Approximation of the boundary in the finite element solution of fourth order problems, SIAM J. Numer. Anal. 15 (1978), no. 3, 568–579. MR 471373, DOI 10.1137/0715037
Miloš Zlámal, Curved elements in the finite element method. I, SIAM J. Numer. Anal. 10 (1973), 229–240. MR 395263, DOI 10.1137/0710022