Stenberg’s sufficiency criteria for the LBB condition for axisymmetric Stokes flow

Abstract

In this article we investigate the LBB condition for axisymmetric flow problems. Specifically, the sufficiency condition for approximating pairs to satisfy the LBB condition established by Stenberg in the Cartesian coordinate setting is presented for the cylindrical coordinate setting. For the cylindrical coordinate setting, the Taylor–Hood (k=2) and conforming Crouzeix–Raviart elements are shown to be LBB stable. A priori error bounds for approximations to the axisymmetric Stokes flow problem using Taylor–Hood and Crouzeix–Raviart elements are given. The computed numerical convergence rates for the error for an axisymmetric Stokes flow problem support the theoretical results.