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

Abstract

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 and prove its convergence. The use of weighted Sobolev spaces to treat the discontinuity 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.