First-Order System Least Squares (FOSLS) for Spatial Linear Elasticity: Pure Traction

2000 ◽  
Vol 38 (5) ◽  
pp. 1454-1482 ◽  
Author(s):  
Sang Dong Kim ◽  
Thomas A. Manteuffel ◽  
Stephen F. McCormick
Keyword(s):  
Least Squares ◽  
Linear Elasticity ◽  
Order System ◽  
First Order

First-Order System Least Squares For Linear Elasticity: Numerical Results

2000 ◽  
Vol 21 (5) ◽  
pp. 1706-1727 ◽  
Author(s):  
Z. Cai ◽  
C. O. Lee ◽  
T. A. Manteuffel ◽  
S. F. McCormick
Keyword(s):  
Least Squares ◽  
Linear Elasticity ◽  
Numerical Results ◽  
Order System ◽  
First Order

scholarly journals First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem

1998 ◽  
Vol 35 (1) ◽  
pp. 320-335 ◽  
Author(s):  
Zhiqiang Cai ◽  
Thomas A. Manteuffel ◽  
Stephen F. McCormick ◽  
Seymour V. Parter
Keyword(s):  
Least Squares ◽  
Linear Elasticity ◽  
Order System ◽  
First Order

scholarly journals Nested Iteration and First-Order System Least Squares for Incompressible, Resistive Magnetohydrodynamics

2010 ◽  
Vol 32 (3) ◽  
pp. 1506-1526 ◽  
Author(s):  
J. H. Adler ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. W. Ruge ◽  
G. D. Sanders
Keyword(s):  
Least Squares ◽  
Order System ◽  
First Order ◽  
Nested Iteration

scholarly journals Further results on a space-time FOSLS formulation of parabolic PDEs

2020 ◽  
Author(s):  
Gregor Gantner ◽  
Rob Stevenson
Keyword(s):  
Finite Element Method ◽  
Least Squares ◽  
Parabolic Equations ◽  
Space Time ◽  
Adaptive Finite Element Method ◽  
Order System ◽  
Well Posedness ◽  
Adaptive Finite Element ◽  
Parabolic Pdes ◽  
First Order

In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer&Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven.  In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated.  The proof of the latter easily extends to a large class of least-squares formulations.

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