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The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit $C^1$-elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform $V_{Oh}$-ellipticity are found.

Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector $r={(r_0,...,r_{n-1})}^T$ with respect to the operations $𝒜$, $ℒ$ and to the smoothing parameter $\alpha$. The resulting function is denoted by ${\sigma }_{\alpha }\left(t\right)$. The measured sample $r$ is defined on an equally spaced mesh $\Delta ={\{t_i=ih\}}_{i=0}^{n-1}$ $T=nh$. The smoothed data vector $y$ is then $y={\left\{{\sigma }_{\alpha }\left(t_i\right)\right\}}_{i=0}^{n-1}$. The other operation...