Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Least-square finite elements for Stokes problem
Computer Methods in Applied Mechanics and Engineering
Least-squares finite element method for fluid dynamics
Computer Methods in Applied Mechanics and Engineering
Analysis of least squares finite element methods for the Stokes equations
Mathematics of Computation
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
Preconditioning in H(div) and applications
Mathematics of Computation
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Issues Related to Least-Squares Finite Element Methods for the Stokes Equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
A Least-Squares Spectral Element Formulation for the Stokes Problem
Journal of Scientific Computing
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Parallel Implementation of a Least-Squares Spectral Element Solver for Incompressible Flow Problems
The Journal of Supercomputing
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
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
Mathematics and Computers in Simulation
Journal of Computational Physics
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution
Journal of Computational Physics
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Least-squares spectral element methods are based on two important and successful numerical methods: spectral/hp element methods and least-squares finite element methods. In this respect, least-squares spectral element methods seem very powerful since they combine the generality of finite element methods with the accuracy of the spectral methods and also have the theoretical and computational advantages of the least-squares methods. These features make the proposed method a competitive candidate for the solution of large-scale problems arising in scientific computing. In order to demonstrate its competitiveness, the method has been applied to an analytical problem and the theoretical optimal and suboptimal a priori estimates have been confirmed for various boundary conditions. Moreover, the exponential convergence rates, typical for a spectral element discretization, have also been confirmed. The comparison with the classical Galerkin spectral element method revealed that the least-squares spectral element method is as accurate as the Galerkin method for the smooth model problem.