A high accuracy spectral method based on min/max principle for biharmonic eigenvalue problems on a spherical domain

Abstract

In this study, we develop a high accuracy spectral method based on the min/max principle for biharmonic eigenvalue problems in the spherical domain. By analyzing the orthogonal spherical harmonic and approximation and using the min/max principle, we first deduce the error estimates of approximate eigenvalues. Then we construct an appropriate set of orthogonal spherical functions contained in H02(Ω) and establish the matrix formulations for the discrete variational form, whose mass matrix and stiff matrix are all sparse so that we can solve the numerical solutions efficiently. Finally, we provide some numerical experiments to validate that the theoretical results are correct.