The Finite Element Discretization for Stream-Function Problems on Multiply Connected Domains

The no-normal-flow condition states that the stream-function is constant at solid boundaries. For multiply connected domains these (unknown) constants differ per boundary and must be determined from integral conditions. This complicates discretization and solution of the problem considerably. In this paper we describe a simple, elegant, and systematic way for solving this problem within the context of a finite element discretization and apply our ideas to global ocean circulation simulation.