A second order in time modified Lagrange–Galerkin finite element method for the incompressible Navier-Stokes equations. (English) Zbl 1263.76040
Summary: We introduce a second order in time modified Lagrange-Galerkin (MLG) method for the time dependent incompressible Navier-Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the \(P2/P1\) Taylor-Hood element are used.
MSC:
76M10 | Finite element methods applied to problems in fluid mechanics |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |