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

C. Bacuta, J.H. Bramble, and J.E. Pasciak

We consider the the interpolation problem between $H^2(\d)\cap H^1_D(\d)$ and $H^1_D(\d)$, where $\d$ is a polygonal domain in $\R^2$ and $H^1_D(\Omega) $ is the subspace of functions in $H^1(\Omega) $ which vanish on the Dirichlet part $\gD$ of the boundary of $\d$. The main result is that the interpolation spaces $[H^2(\d)\cap H^1_D(\d), H^1_D(\d)]_s$ and $H^{1+s}(\d)\cap H^1_D(\d) $ coincide. An application of this result to a nonconforming finite element problem is presented.

Thanks: This work was partially supported by the National Science Foundation under Grant DMS-9973328.