A finite element analysis of a pseudostress formulation for the Stokes eigenvalue problem

作者：Meddahi Salim; Mora David^*; Rodriguez Rodolfo

来源：IMA Journal of Numerical Analysis, 2015, 35(2): 749-766.

DOI：10.1093/imanum/dru006

• Stokes equations
• pseudostress
• eigenvalue problem
• mixed finite elements
• error estimates

In this paper we analyse a finite element approximation of the Stokes eigenvalue problem. We introduce a variational formulation relying only on the pseudostress tensor and propose a discretization by means of the lowest-order Brezzi-Douglas-Marini mixed finite element. However, similar results hold true for other H(div)-conforming elements, like Raviart-Thomas elements. We show that the resulting scheme provides a correct approximation of the spectrum and prove optimal-order error estimates. Finally, we report some numerical tests supporting our theoretical results.

• 出版日期2015-4