Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
Journal of Computational Physics
Comparison of finite-volume numerical methods with staggered and colocated grids
Computers and Fluids
Analysis of a multigrid Stokes solver
Applied Mathematics and Computation
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Analysis and convergence of the MAC scheme. I: The linear problem
SIAM Journal on Numerical Analysis
Accelerated multigrid convergence and high-Reynolds recirculating flows
SIAM Journal on Scientific Computing
Analysis and convergence of the MAC scheme. II: Navier-Stokes equations
Mathematics of Computation
An efficient smoother for the Stokes problem
Applied Numerical Mathematics - Special issue on multilevel methods
A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations
SIAM Journal on Numerical Analysis
Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Multigrid
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Block Preconditioners Based on Approximate Commutators
SIAM Journal on Scientific Computing
Multigrid Methods for the Stokes System
Computing in Science and Engineering
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
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A distributive Gauss---Seidel relaxation based on the least squares commutator is devised for the saddle-point systems arising from the discretized Stokes equations. Based on that, an efficient multigrid method is developed for finite element discretizations of the Stokes equations on both structured grids and unstructured grids. On rectangular grids, an auxiliary space multigrid method using one multigrid cycle for the Marker and Cell scheme as auxiliary space correction and least squares commutator distributive Gauss---Seidel relaxation as a smoother is shown to be very efficient and outperforms the popular block preconditioned Krylov subspace methods.