An $H_0^m $ Interpolation Result
S. Jensen · SIAM Journal on Mathematical Analysis · 1991
This paper presents a proof of an interpolation result related to the approximation theory for higher-order finite element or spectral methods when $C^1$ (or higher) regularity is convenient for the finite-dimensional subspaces. This can be a natural choice, for example, for the Stokes problem, the biharmonic problem, or higher-order plate and shell models. It is shown that the same intermediate spaces are obtained whether one (1) interpolates between two Sobolev spaces defined on a domain with nonsmooth boundary first and then enforces the homogeneous boundary conditions afterwards or (2) interpolates between two Sobolev spaces where the homogeneous boundary conditions are enforced throughout the interpolation process.