×

A term by term stabilization algorithm for finite element solution of incompressible flow problems. (English) Zbl 0910.76033

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.

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
PDFBibTeX XMLCite
Full Text: DOI