scholarly journals New a priori analysis of first‐order system least‐squares finite element methods for parabolic problems

2019 ◽  
Vol 35 (5) ◽  
pp. 1777-1800
Author(s):  
Thomas Führer ◽  
Michael Karkulik
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
A Priori ◽  
Order System ◽  
Parabolic Problems ◽  
First Order ◽  
A Priori Analysis

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

DISCONTINUOUS/CONTINUOUS LEAST-SQUARES FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS

2005 ◽  
Vol 15 (06) ◽  
pp. 825-842 ◽  
Author(s):  
RICKARD E. BENSOW ◽  
MATS G. LARSON
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
A Priori Estimates ◽  
A Priori ◽  
Solution Space ◽  
First Order ◽  
Poisson Problem ◽  
Priori Estimates ◽  
The Stability

Least-squares finite element methods (LSFEM) are useful for first-order systems, where they avoid the stability consideration of mixed methods and problems with constraints, like the div-curl problem. However, LSFEM typically suffer from requirements on the solution to be very regular. This rules out, e.g., applications posed on nonconvex domains. In this paper we study a least-squares formulation where the discrete space is enriched by discontinuous elements in the vicinity of singularities. The weighting on the interelement terms are chosen to give correct regularity of the solution space and thus making computation of less regular problems possible. We apply this technique to the first-order Poisson problem, show coercivity and a priori estimates, and present numerical results in 3D.

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