Chacón Rebollo, Tomás A term by term stabilization algorithm for finite element solution of incompressible flow problems. (English) Zbl 0910.76033 Numer. Math. 79, No. 2, 283-319 (1998). Summary: This paper introduces a stabilization technique for finite element numerical solution of two- and three-dimensional incompressible flow problems. It can be applied to stabilize the discretization of the pressure gradient, and also of any individual operator term such as the convection, curl or divergence operators, with specific levels of numerical diffusion for each of them. Its computational complexity is reduced with respect to usual (residual-based) stabilization techniques. We consider piecewise affine finite elements, for which we obtain optimal error bounds for steady Navier-Stokes and generalized Stokes equations (including convection). We include some numerical experiments in well-known two-dimensional test cases, that show a good performance of the method. Cited in 3 ReviewsCited in 30 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76D07 Stokes and related (Oseen, etc.) flows Keywords:discretization of pressure gradient; piecewise affine finite elements; optimal error bounds PDFBibTeX XMLCite \textit{T. Chacón Rebollo}, Numer. Math. 79, No. 2, 283--319 (1998; Zbl 0910.76033) Full Text: DOI