Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions∗∗∗∗
نویسندگان
چکیده
The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C elements for velocity and C elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.
منابع مشابه
Weighted Inf-sup Condition and Pointwise Error Estimates for the Stokes Problem
Convergence of mixed finite element approximations to the Stokes problem in the primitive variables is examined in maximum norm. Quasioptimal pointwise error estimates are derived for discrete spaces satisfying a weighted inf-sup condition similar to the Babuska -Brezzi condition. The usual techniques employed to prove the inf-sup condition in energy norm can be easily extended to the present s...
متن کاملError Estimates for Finite Element Approximations of Consistent Splitting Schemes for Incompressible Flows
We study a finite element approximation for the consistent splitting scheme proposed in [11] for the time dependent Navier-Stokes equations. At each time step, we only need to solve a Poisson type equation for each component of the velocity and the pressure. We cast the finite element approximation in an abstract form using appropriately defined discrete differential operators, and derive optim...
متن کاملNumerical Analysis and Scientific Computing Preprint Seria Inf-sup stability of geometrically unfitted Stokes finite elements
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a class of unfitted finite element methods for the Stokes and Stokes interface problems, such as Nitsche-XFEM or cutFEM. The error analysis is presented for the ...
متن کامل10th International Workshop on Variational Multiscale and Stabilized Finite Elements (VMS2015)
for 10th International Workshop on Variational Multiscale and Stabilized Finite Elements (VMS2015) Some open problems of inf-sup stable FEM for incompressible flow problems G. Lube∗ Georg-August University Göttingen, Institute for Numerical and Applied Mathematics [email protected] In this talk, I will address some open problems occuring in the numerical approximation of incompressibl...
متن کاملError analysis of fully discrete velocity-correction methods for incompressible flows
A fully discrete version of the velocity-correction method, proposed by Guermond and Shen (2003) for the time-dependent Navier-Stokes equations, is introduced and analyzed. It is shown that, when accounting for space discretization, additional consistency terms, which vanish when space is not discretized, have to be added to establish stability and optimal convergence. Error estimates are deriv...
متن کامل