Edge behaviour of the solution of the Stokes problem with applications to the finite-element method

The Stokes problem on a domain with edge singularities is considered. The d ecomposition of the solution into a regular part and blocks of singular fun ctions is established. This, together with the tangential regularity of the solution, leads to a global regularity result in suitable weighted Sobolev spaces, the properties of which are investigated. The global regularity is exploited to generate an optimally convergent semi-discrete mesh refinemen t mixed finite-element method. In the particular case of a prismatic domain , the Fourier finite-element method, which is a fully discrete scheme, is i mplemented.