Fully Discrete Method for the Boundary Integral Equations of Eigenvalue Problems

In this paper, the fully discrete method is applied for the eigensolutions of the Laplace equation on smooth closed boundaries. The fully discrete method mainly consists of two levels of numerical quadrature: the trapezoidal rule for the integrals including the weakly singularity, and the discrete inner product for the outer integrals. The convergence and error results of the fully discrete method for Steklov eigenvalue problems are provided. Thereafter, the numerical examples demonstrate the efficiency of the fully discrete method.