turkmath.org

The talk deals with numerical solution strategies for the Stokes eigenvalue problem based on penalty techniques. In general, when the task is to approximate the eigenmodes of the Stokes problem formulated in primitive variables, velocity and pressure, major difficulties arise not only due to the fact that the discretization of the operator leads to a generalized eigenvalue problem, but also due to the existence of zero diagonal entries in the resulting algebraic system. In this talk, we will investigate the possibility of utilizing the penalty method approach for approximating the eigensolutions of the Stokes operator, by rectifying these issues. The implementation of two different schemes, namely, the standard penalization with a small penalty parameter, and the iterative penalization that enables relatively large parameters will be discussed. Concerning the spatial discretization, among other possible options, the Chebyshev collocation method based on expanding the unknown fields in tensor product of Chebyshev polynomials will be presented.