A high order term-by-term stabilization solver for incompressible flow problems. (English) Zbl 1426.76234
Summary: In this paper, we introduce a low-cost, high-order stabilized method for the numerical solution of incompressible flow problems. This is a particular type of projection-stabilized method where each targeted operator, such as the pressure gradient or the convection, is stabilized by least-squares terms added to the Galerkin formulation. The main methodological originality is that we replace the projection-stabilized structure by an interpolation-stabilized structure, with reduced computational cost for some choices of the interpolation operator. This stabilization has one level, in the sense that it is defined on a single mesh. We prove the stability of our formulation by means of a specific inf-sup condition, which is the main technical innovation of our paper. We perform a convergence and error estimates analysis, proving the optimal order of accuracy of our method. We include some numerical tests that confirm our theoretical expectations.
MSC:
76M10 | Finite element methods applied to problems in fluid mechanics |
76D05 | Navier-Stokes equations for incompressible viscous fluids |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |