The element separation property and parallel finite element methods for the Navier-Stokes equation Original Research Article

This report considers the amount of parallelism attainable in certain robust domain decomposition methods for linearizations of the Navier-Stokes equations. The connection between parallelism and the finite element basis is shown in terms of the separation property of that basis, introduced in Section 2. Section 3 studies these questions in particular for the Navier-Stokes equations. Section 3 resolves the separation properties of common, low order spaces which satisfy the inf-sup condition, as well as introduces a new, low order space which has the (optimal) element separation property.