scholarly journals A first order system least squares method for the Helmholtz equation

2017 ◽  
Vol 309 ◽  
pp. 145-162 ◽  
Author(s):  
Huangxin Chen ◽  
Weifeng Qiu
Keyword(s):  
Helmholtz Equation ◽  
Least Squares ◽  
Least Squares Method ◽  
Order System ◽  
First Order

A Fluidity-Based First-Order System Least-Squares Method for Ice Sheets

2017 ◽  
Vol 39 (2) ◽  
pp. B352-B374 ◽  
Author(s):  
Jeffery Allen ◽  
Chris Leibs ◽  
Tom Manteuffel ◽  
Harihar Rajaram
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Ice Sheets ◽  
Order System ◽  
First Order

A First-Order System Least Squares Method for Hyperelasticity

2014 ◽  
Vol 36 (5) ◽  
pp. B795-B816 ◽  
Author(s):  
Benjamin Müller ◽  
Gerhard Starke ◽  
Alexander Schwarz ◽  
Jörg Schröder
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Order System ◽  
First Order

scholarly journals First-Order System Least-Squares for the Helmholtz Equation

2000 ◽  
Vol 21 (5) ◽  
pp. 1927-1949 ◽  
Author(s):  
B. Lee ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. Ruge
Keyword(s):  
Helmholtz Equation ◽  
Least Squares ◽  
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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