Local And Parallel Finite Element Schemes For The Biharmonic Eigenvalue Problem Of Plate Buckling

Biharmonic eigenvalue problem of plate buckling is an important problem in elastic mechanics and has been widely used in mechanical manufacturing,structural engineer-ing and other fields.Its eigenvalues represent the buckling load which can reflect the bearing capacity of the plate.They have high reference value in practical engineering and have been concerned by many scholars.Local and parallel computation is one of the mainstreams in scientific computing and can effectively deal with the problem of large computation and long time-consuming when solving eigenvalue problems.It is a powerful tool to compute eigenvalues.In this paper,we study the local and parallel finite element algorithms for the bi-harmonic eigenvalue problem of plate buckling.Firstly,we analyze the local prior error estimates of finite element approximations for the biharmonic eigenvalue problem of plate buckling.Secondly,we use the the local defect correction method to establish the three-scale and multiscale discretization schemes based on local computation and prove the error estimates of the schemes.After that,we design the multiscale discretization scheme based on parallel computation and obtain its error estimates.Finally,we carry out some numerical experiments on the L-shaped domain and the slit domain,and compare the numerical results of three-scale scheme,multiscale scheme and~2-conforming spectral element method.Theoretical analysis and numerical experiments indicate that the local and parallel finite element multiscale discretization schemes are suitable and efficient for eigenfunctions with local low smoothness.