Conforming element method and shifted-inverse two-grid dicretization for the fourth-order Steklov eigenvalue problem

The fourth-order Steklov eigenvalue problem is essential in analyzing the supported plate and the deformation of the linear elastic hinge phenomenon. This paper conducts an error analysis of the conforming element method for this problem and subsequently proposes a shifted-inverse two-grid scheme. The optimal convergence order of both methods are established through rigorous proof. Numerical examples are presented on various domains to demonstrate the effectiveness of the proposed two-grid scheme in comparison with solving the eigenvalue problem using a direct solver.