Numerical Assessment of a Class of High Order Stokes Spectrum Solver (Journal of Mathematical Study, 2019)
It is well known that the approximation of eigenvalues and associated eigenfunctionsof a linear operator under constraint is a difficult problem. One of the difficulties is to propose methods of approximation which satisfy in a stable and accurateway the eigenvalues equations, the constraint one and the boundary conditions. Usingany non-stable method leads to the presence of non-physical eigenvalues: a multiplezero one called spurious modes and non-zero one called pollution modes. One way toeliminate these two families is to favor the constraint equations by satisfying it exactlyand to verify the equations of the eigenvalues equations in weak ways. To illustrateour contribution in this field we consider in this paper the case of Stokes operator.We describe several methods that produce the correct number of eigenvalues. Wenumerically prove how these methods are adequate to correctly solve the 2D Stokeseigenvalue problem.