Spectral element discretization of the circular driven cavity, part I: TheLaplace equation

This paper is devoted to the spectral element discretization of the Laplace equation in a disk when provided with discontinuous boundary data. Relying on an appropriate variational formulation, we propose a discrete problem a nd prove its convergence. The use of weighted Sobolev spaces to treat the d iscontinuity of the boundary conditions also allows for improving the order of convergence. The results of the numerical experiments we present are in agreement with the theoretical ones.