Spectral element discretization of the circular driven cavity, Part II: The bilaplacian equation

Abstract

This paper deals with the spectral element discretization of the bilaplacian equation in a disk 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.