DIVERGENCE-FREE KERNEL METHODS FOR APPROXIMATING THE STOKES PROBLEM

摘要

We develop a new discretization scheme for the Stokes equations using analytically divergence-free approximation spaces. Our scheme is based upon a meshfree method using matrix-valued kernels. The scheme works in arbitrary space dimension and can produce arbitrarily smooth and hence high order approximations. After deriving the scheme, we analyze the discretization error in Sobolev spaces and give a numerical example.