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

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.