The macroelement analysis for axisymmetric Stokes equations

We consider the mixed finite element approximation of axisymmetric Stokes problem (ASP) on a bounded polygonal domain in rz-plane. Standard stability results methods do not apply due to singular coefficients differential operator and or vanishing weights associated function spaces. develop new analysis these weighted spaces, propose macroelement conditions that are sufficient ensure well-posedness for ASP. These local, relatively easy verify, therefore will be useful validating variety methods. can only re-verify existing stable ASP, but also lead discovery conservative report numerical test confirm theory.