Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations

2011 ◽  
Vol 33 (1) ◽  
pp. 1-24 ◽  
Author(s):  
J. H. Adler ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. W. Nolting ◽  
J. W. Ruge ◽  
...  
Keyword(s):  
Least Squares ◽  
Order System ◽  
Local Refinement ◽  
First Order ◽  
Adaptive Local Refinement

scholarly journals Further results on error estimators for local refinement with first-order system least squares (FOSLS)

2010 ◽  
Vol 17 (2-3) ◽  
pp. 387-413 ◽  
Author(s):  
Thomas Manteuffel ◽  
Steven McCormick ◽  
Joshua Nolting ◽  
John Ruge ◽  
Geoff Sanders
Keyword(s):  
Least Squares ◽  
Order System ◽  
Local Refinement ◽  
Error Estimators ◽  
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.

Hybrid First-Order System Least Squares Finite Element Methods with Application to Stokes Equations

2013 ◽  
Vol 51 (4) ◽  
pp. 2214-2237 ◽  
Author(s):  
K. Liu ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. W. Ruge ◽  
L. Tang
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Stokes Equations ◽  
Order System ◽  
First Order

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 on Curved Boundaries: Higher-order Raviart--Thomas Elements

2014 ◽  
Vol 52 (6) ◽  
pp. 3165-3180 ◽  
Author(s):  
Fleurianne Bertrand ◽  
Steffen Münzenmaier ◽  
Gerhard Starke
Keyword(s):  
Least Squares ◽  
Higher Order ◽  
Order System ◽  
Curved Boundaries ◽  
First Order
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