Abstract
In this work, an efficient Legendre spectral element method was proposed to solve the two‐dimensional Stokes eigenvalue problem on L‐shaped domain. Based on minimax principle, the rigorous error estimates of the approximate eigenvalues are proved. The approximate eigenvalues converge with the order
O(h2min(N−1,s−2)N2(2−s)) in L2 norm, where h,N, and s are space grid size, polynomial degree, and the regularity of exact solution, respectively. Several numerical examples are provided to verify the theoretical analysis and demonstrate the effectiveness of the proposed scheme.