2016/10/27 by Jing An, Huiyuan Li, An, Jing +3
Computer Science · Engineering · #35Q40 #65N25 #65N35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1610.08647
openalex publication_date 2016/10/27 · openalex created_date 2016/11/04 · openalex updated_date 2026/08/01
In this paper we propose and analyze spectral-Galerkin methods for the Stokes eigenvalue problem based on the stream function formulation in polar geometries. We first analyze the stream function formulated fourth-order equation under the polar coordinates, then we derive the pole condition and reduce the problem on a circular disk to a sequence of equivalent one-dimensional eigenvalue problems that can be solved in parallel. The novelty of our approach lies in the construction of suitably weighted Sobolev spaces according to the pole conditions, based on which, the optimal error estimate for approximated eigenvalue of each one dimensional problem can be obtained. Further, we extend our method to the non-separable Stokes eigenvalue problem in an elliptic domain and establish the optimal error bounds. Finally, we provide some numerical experiments to validate our theoretical results and algorithms.