Unsteady solution of incompressible Navier-Stokes equations
Journal of Computational Physics
Matrix computations (3rd ed.)
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Basis Functions for Triangular and Quadrilateral High-Order Elements
SIAM Journal on Scientific Computing
Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
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
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Least-squares finite element models of two-dimensional compressible flows
Finite Elements in Analysis and Design
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Mass- and Momentum Conservation of the Least-Squares Spectral Element Method for the Stokes Problem
Journal of Scientific Computing
Journal of Scientific Computing
Higher-Order Gauss---Lobatto Integration for Non-Linear Hyperbolic Equations
Journal of Scientific Computing
Numerical calculation of the moments of the population balance equation
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Least-squares spectral method for solving advective population balance problems
Journal of Computational and Applied Mathematics
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
Direct Minimization of the least-squares spectral element functional - Part I: Direct solver
Journal of Computational Physics
hp-Adaptive least squares spectral element method for hyperbolic partial differential equations
Journal of Computational and Applied Mathematics
Least-squares spectral element method for non-linear hyperbolic differential equations
Journal of Computational and Applied Mathematics
hp-adaptive least squares spectral element method for population balance equations
Applied Numerical Mathematics
Journal of Computational Physics
Simulation of thermal disturbances with finite wave speeds using a high order method
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational Physics
Simulation of a natural circulation loop using a least squares hp-adaptive solver
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Newton multigrid least-squares FEM for the V-V-P formulation of the Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.49 |
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L2 least-squares functional and L2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares space-time decoupled finite element models. The numerical results show that the space-time coupled formulation has superior predictive capabilities for flows demanding high space-time resolution, exemplified here by the transient flow over a backward-facing step.