Abstract
Some conforming, nonconforming and mixed finite element methods for approximating the clamped plate problem
on ∂Ω, over a bounded plane domain Ω ⊂R2 are considered. Asymptotic L∞-estimates for the error in displacement are established which have the same 0(h)-order as the well known L2-estimates. As in the case of second order problems (see [7]) the proofs rest on estimates for regularized fundamental solutions of the operator Δ2 and its discrete analogues.
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Rannacher, R. Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem. Manuscripta Math 19, 401–416 (1976). https://doi.org/10.1007/BF01278927
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DOI: https://doi.org/10.1007/BF01278927