An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem

Abstract

In this article, an effective finite element method based on dimension reduction scheme is proposed for a fourth-order Steklov eigenvalue problem in a circular domain. By using the Fourier basis function expansion and variable separation technique, the original problem is transformed into a series of radial one-dimensional eigenvalue problems with boundary eigenvalue. Then we introduce essential polar conditions and establish the discrete variational form for each radial one-dimensional eigenvalue problem. Based on the minimax principle and the approximation property of the interpolation operator, we prove the error estimates of approximation eigenvalues. Finally, some numerical experiments are provided, and the numerical results show the efficiency of the proposed algorithm.

Keywords

• fourth-order steklov eigenvalue problem
• weighted sobolev space
• dimension reduction scheme
• finite element approximation
• error estimation
• 34l15
• 65m60
• 97n20