The stability of mixed hp-finite element methods for Stokes flow on high aspect ratio elements

The presence of boundary layers and other localized features in the solutions of incompressible ow problems complicates their accurate numerical approximation. These features may be efficiently resolved through the use of mixed finite element methods using high aspect ratio elements in conjunction with high order polynomial subspaces. The stability of such methods is extremely sensitive to the aspect ratio of the elements and the order of the polynomial spaces used and may be quanti ed by the constant appearing in an inf-sup condition between the velocity and pressure approximation spaces. The present work analyzes the inf-sup constant for families of mixed finite element families on meshes containing high aspect ratio, a ne, quadrilateral elements with emphasis on the dependence of the inf-sup constant on the polynomial degree and the aspect ratio.