New interpolation results and applications to finite element methods for elliptic boundary value problems (Q2763866)

Let \(\Omega\) be a polygonal domain on the real plane and \(H^1_D(\Omega)\) the subspace of functions in \(H^1(\Omega)\) which vanish on the Dirichlet part \((\partial\Omega)_D\) of the boundary of \(\Omega\). The interpolation problem between \(H^2(\Omega)\cap H^1_D(\Omega)\) and \(H^1_D(\Omega)\) is considered. The main result states that the interpolation spaces \([H^2(\Omega)\cap H^1_D(\Omega), H^1_D(\Omega)]_S\) and \(H^{1+s}(\Omega)\cap H^1_D(\Omega)\) coincide. An application of this result to a nonconforming finite element problem is also presented.