Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Issues Related to Least-Squares Finite Element Methods for the Stokes Equations
SIAM Journal on Scientific Computing
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
On mass conservation in least-squares methods
Journal of Computational Physics
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
A least-squares finite element method for the Navier-Stokes equations
Journal of Computational Physics
On Mass-Conserving Least-Squares Methods
SIAM Journal on Scientific Computing
A monolithic FEM-multigrid solver for non-isothermal incompressible flow on general meshes
Journal of Computational Physics
Weighted least-squares finite elements based on particle imaging velocimetry data
Journal of Computational Physics
Enhanced Mass Conservation in Least-Squares Methods for Navier-Stokes Equations
SIAM Journal on Scientific Computing
New robust nonconforming finite elements of higher order
Applied Numerical Mathematics
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We solve the V-V-P, vorticity-velocity-pressure, formulation of the stationary incompressible Navier-Stokes equations based on the least-squares finite element method. For the discrete systems, we use a conjugate gradient (CG) solver accelerated with a geometric multigrid preconditioner for the complete system. In addition, we employ a Krylov space smoother inside of the multigrid which allows a parameter-free smoothing. Combining this linear solver with the Newton linearization, we construct a very robust and efficient solver. We use biquadratic finite elements to enhance the mass conservation of the least-squares method for the inflow-outflow problems and to obtain highly accurate results. We demonstrate the advantages of using the higher order finite elements and the grid independent solver behavior through the solution of three stationary laminar flow problems of benchmarking character. The comparisons show excellent agreement between our results and those of the Galerkin mixed finite element method as well as available reference solutions.