Least squares finite element simulation of transonic flows
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
A finite element method for first order elliptic systems in three dimensions
Applied Mathematics and Computation
Least-square finite elements for Stokes problem
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Optimal least-squares finite element method for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Analysis of least squares finite element methods for the Stokes equations
Mathematics of Computation
Least-squares mixed finite elements for second-order elliptic problems
SIAM Journal on Numerical Analysis
Least-squares methods for Stokes equations based on a discrete minus one inner product
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
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
A negative-norm least squares method for Reissner-Mindlin plates
Mathematics of Computation
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
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
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A new least-squares finite element method is analyzed for the thin plate problem subject to various boundary conditions (clamped, simply supported and free). The unknown variables are deflection, slope, moment and shear force. The coercivity property is established. As a result, all variables can be approximated by any conforming finite elements. In particular, an H^1-ellipticity is proven for the free thin plate. This indicates that optimal error bounds hold for all variables with the use of equal-order continuous elements. Numerical experiments are performed to confirm the theoretical results obtained.