Quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle. (Q1871514)

Let \(\Omega\) be a bounded domain of \(\mathbb{R}^{2}\) with smooth boundary \(\partial\Omega,\) \(f\in L^{2}(\Omega)\) and \(\phi\in H^{4}(\Omega)\) with \(\phi<0\) on \(\partial\Omega\). Set \(K=\{v\in H_{0}^{2}(\Omega) \mid v\geq\phi\}\) and let \(u\in K\) be a solution of the variational inequality problem \[ \int_{\Omega}\Delta u\Delta(v-u)dx\geq\int_{\Omega}f(v-u)dx,\text{\quad }\forall v\in K \] The authors apply ``unconventional quasi-conforming'' finite element approximation on the above problem. They assert to obtain error estimates which are the same as that of the conventional finite elements.