New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem (Journal of Computational Mathematics, 2018)
This paper is concerned with the finite elements approximation for the Steklov eigenvalueproblem on concave polygonal domain. We make full use of the regularity estimateand 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 eigenfunctionof linear conforming finite element and the nonconforming Crouzeix-Raviart element.Finally, we present some numerical results to support the theoretical analysis.
Keywords: Steklov eigenvalue problem; Concave polygonal domain; Linear conforming finite element; Nonconforming Crouzeix-Raviart element; Error estimates.