Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization
Journal of Scientific Computing
A Least-Squares Spectral Element Formulation for the Stokes Problem
Journal of Scientific Computing
Analysis of a Discontinuous Least Squares Spectral Element Method
Journal of Scientific Computing
Parallel Implementation of a Least-Squares Spectral Element Solver for Incompressible Flow Problems
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Journal of Computational and Applied Mathematics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Nonconforming elements in least-squares mixed finite element methods
Mathematics of Computation
Parallel Implementation of a Least-Squares Spectral Element Solver for Incompressible Flow Problems
The Journal of Supercomputing
Least-squares finite element models of two-dimensional compressible flows
Finite Elements in Analysis and Design
Journal of Computational Physics
Analysis of [H-1,L2,L2] first-order system least squares for the incompressible Oseen type equations
Applied Numerical Mathematics
On mass conservation in least-squares methods
Journal of Computational Physics
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational and Applied Mathematics
Higher-Order Gauss---Lobatto Integration for Non-Linear Hyperbolic Equations
Journal of Scientific Computing
A least-squares finite element method for the Navier-Stokes equations
Journal of Computational Physics
Analysis of a splitting method for incompressible inviscid rotational flow problems
Journal of Computational and Applied Mathematics
A unified least-squares formulation for fluid-structure interaction problems
Computers and Structures
A least-squares/penalty method for distributed optimal control problems for Stokes equations
Computers & Mathematics with Applications
Direct Minimization of the least-squares spectral element functional - Part I: Direct solver
Journal of Computational Physics
A convergence result for a least-squares method using Schauder bases
Mathematics and Computers in Simulation
Least-squares spectral element method for non-linear hyperbolic differential equations
Journal of Computational and Applied Mathematics
Analysis and computation of a least-squares method for consistent mesh tying
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Adjoint pseudospectral least-squares methods for an elliptic boundary value problem
Applied Numerical Mathematics
Analysis of a least-squares finite element method for the thin plate problem
Applied Numerical Mathematics
Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Weighted least-squares finite elements based on particle imaging velocimetry data
Journal of Computational Physics
A least squares coupling method with finite elements and boundary elements for transmission problems
Computers & Mathematics with Applications
Least-squares finite-element methods for optimization and control problems for the stokes equations
Computers & Mathematics with Applications
Least squares finite element methods for fluid-structure interaction problems
Computers and Structures
A nonlinear weighted least-squares finite element method for Stokes equations
Computers & Mathematics with Applications
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational and Applied Mathematics
Least-squares finite element methods for generalized Newtonian and viscoelastic flows
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Computational Physics
The automatic construction and solution of a partial differential equation from the strong form
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
A least-squares fem-bem coupling method for linear elasticity
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Goal-Oriented Local A Posteriori Error Estimators for H(div) Least-Squares Finite Element Methods
SIAM Journal on Numerical Analysis
The least-squares pseudo-spectral method for Navier-Stokes equations
Computers & Mathematics with Applications
Journal of Computational Physics
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We consider the application of least-squares variational principles to the numerical solution of partial differential equations. Our main focus is on the development of least-squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows, linear elasticity, and convection-diffusion. For many of these problems, least-squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods that are not present in standard Galerkin discretizations. Most notably, the use of least-squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf-sup condition arising in mixed methods for the Stokes and Navier--Stokes equations. As a result, application of least-squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance.