Quasi-Norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems

Abstract

In this work, new interpolation error estimates have been derived for some well-known interpolators in the quasi-norms. The estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations. In particular, by using these estimates, we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2-d and 3-d p-Laplacian.