Numerical Method For Two-dimensional Elliptic Eigenvalue Problem With Discontinuous Coefficients

This paper aims to solve the eigenvalue problem of a two-dimensional elliptic equation with transmission conditions and discontinuous coefficients.First,this paper proves some basic properties of the equation,which include that its eigenvalues are all real numbers,the eigenfunctions are orthogonal for different eigenvalues.Second,error analysis is carried out for the eigenvalues and the numerical solutions of the eigenfunctions.Third,numerical examples are utilized to verify and further analyze the results.Among the numerical results,the numerical experimental error results are consistent with the theoretical error analysis results.It is found that when the coefficient is discontinuous,the accuracy of spectral method will drop.Also,for spectral method,numerical experiments indicate that the first half part of the eigenvalues obtained by the algorithm is reliable with a smaller error,but the error of the later larger-half part is larger and larger and thus the latter part is not reliable.In addition,the experimental results verify the orthogonality of eigenfunctions based on different eigenvalues.