A fictitious domain/finite element method for particulate flows
Journal of Computational Physics
A new class of truly consistent splitting schemes for incompressible flows
Journal of Computational Physics
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A grid-alignment finite element technique for incompressible multicomponent flows
Journal of Computational Physics
Error estimate of a first-order time discretization scheme for the geodynamo equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Open and traction boundary conditions for the incompressible Navier-Stokes equations
Journal of Computational Physics
Error estimates for an operator-splitting method for Navier-Stokes equations: Second-order schemes
Journal of Computational and Applied Mathematics
An unconditionally stable rotational velocity-correction scheme for incompressible flows
Journal of Computational Physics
Journal of Computational Physics
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
Journal of Computational Physics
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
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We introduce and study a new class of projection methods---namely, the velocity-correction methods in standard form and in rotational form---for solving the unsteady incompressible Navier--Stokes equations. We show that the rotational form provides improved error estimates in terms of the H1-norm for the velocity and of the L2-norm for the pressure. We also show that the class of fractional-step methods introduced in [S. A. Orsag, M. Israeli, and M. Deville, J. Sci. Comput., 1 (1986), pp. 75--111] and [K. E. Karniadakis, M. Israeli, and S. A. Orsag, J. Comput. Phys., 97 (1991), pp. 414--443] can be interpreted as the rotational form of our velocity-correction methods. Thus, to the best of our knowledge, our results provide the first rigorous proof of stability and convergence of the methods in those papers. We also emphasize that, contrary to those of the above groups, our formulations are set in the standard L2 setting, and consequently they can be easily implemented by means of any variational approximation techniques, in particular the finite element methods.