Local a priori/a posteriori error estimates of conforming finite elements approximation for Steklov eigenvalue problems

Abstract

Based on the work of Xu and Zhou (2000), this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems, and proves a local a priori error estimate and a new local a posteriori error estimate in \(\left\| \cdot \right\|_{1,\Omega _0 }\) norm for conforming elements eigenfunction, which has not been studied in existing literatures.