New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem

Abstract

This paper is concerned with the finite elements approximation for the Steklov eigenvalue problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix-Raviart element, and prove a new and optimal error estimate in $‖·‖_{0,∂Ω}$ for the eigenfunction of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.