Abstract
We propose a characteristic Galerkin scheme using B-spline basis functions based on a mixed formulation for incompressible flows which is capable of being second-order accurate in time. One of significant features of the B-spline basis functions is that the B-spline basis functions of p degrees have at most Cp−1 continuous derivatives although classical finite elements based on Lagrange polynomials have only C0 continuous derivatives. We use the mixed formulation to velocity and pressure fields, which satisfies the inf-sup condition. The velocity element is obtained by a subgrid of the pressure element. The pair of the pressure and velocity elements is referred to as the subgrid (SG) element, and it allows for both velocity and pressure at the highest regularity. In order to confirm effectivity of the present scheme, we perform some numerical experiments.
