Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
H-1 least-squares method for the velocity-pressure-stress formulation of Stokes equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
A numerical model of stress driven grain boundary diffusion
Journal of Computational Physics
First-order system least squares (FOSLS) for coupled fluid-elastic problems
Journal of Computational Physics
Journal of Computational Physics
On mass conservation in least-squares methods
Journal of Computational Physics
The Optimisation of the Mesh in First-Order Systems Least-Squares Methods
Journal of Scientific Computing
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A remark on least-squares mixed element methods for reaction-diffusion problems
Journal of Computational and Applied Mathematics
A least-squares/penalty method for distributed optimal control problems for Stokes equations
Computers & Mathematics with Applications
Analysis of a least-squares finite element method for the thin plate problem
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Least squares finite element methods for fluid-structure interaction problems
Computers and Structures
Journal of Computational and Applied Mathematics
A posteriori error estimators for the first-order least-squares finite element method
Journal of Computational and Applied Mathematics
The least-squares pseudo-spectral method for Navier-Stokes equations
Computers & Mathematics with Applications
Journal of Computational Physics
Hi-index | 0.05 |
Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H1 product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are naturally uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity, where we obtain the more substantive result that the estimates are uniform in the Poisson ratio.