Amara, Mohamed; Bernardi, Christine Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation. (English) Zbl 0956.76040 M2AN, Math. Model. Numer. Anal. 33, No. 5, 1033-1056 (1999). Summary: The standard discretization of the Stokes and Navier-Stokes equations in vorticity and stream function formulation by affine finite elements is known for its bad convergence. We present here a modified discretization, prove that the convergence is improved, and establish a priori error estimates. Cited in 1 ReviewCited in 14 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D07 Stokes and related (Oseen, etc.) flows 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs Keywords:improved convergence; Stokes equations; stream function and vorticity formulation; well-posedness; mortar element discretization; higher-order discretizations; Navier-Stokes equations; affine finite elements; a priori error estimates PDFBibTeX XMLCite \textit{M. Amara} and \textit{C. Bernardi}, M2AN, Math. Model. Numer. Anal. 33, No. 5, 1033--1056 (1999; Zbl 0956.76040) Full Text: DOI EuDML Link