Abstract
In the problem of incompressible media such as the Stokes flow or incompressible elasticity, the mixed finite element approximation employing the MINI element, in which the velocity field is approximated by P1 field and bubble function and pressure is approximated by P1 continuous field, is known as one of those satisfying the inf-sup (or LBB) condition. Recently, it has been shown that the MINI element is equivalent to a stabilized finite element by P1-P1approximation with pressure stabilization term. In this aspect, the stabilizing effect of the MINI element is evaluated by stabilizing parameter determined by the shape of the bubble function. In this work, the numerical stability of the bubble elements including the nonconforming elements in two and three dimensional problems is evaluated in the sense of the stabilized method.
