New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity

Abstract

In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon Ω with an internal corner ω greater than 180 ∘ on its boundary is presented. The results of computational simulations have shown that the convergence rate of the approximate solution (velocity field) by weighted FEM to the exact solution does not depend on the value of the internal corner ω and equals O ( h ) in the norm of a space W 2 , ν 1 ( Ω ) .

Keywords

• Oseen problem
• corner singularity
• weighted finite element method
• preconditioning