Extraction methods for second derivatives in finite element approximations of linear elasticity problems

1985 ◽  
Vol 1 (3) ◽  
pp. 137-139 ◽  
Author(s):  
L. Demkowicz ◽  
J. T. Oden
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Extraction Methods ◽  
Finite Element Approximations ◽  
Second Derivatives ◽  
Elasticity Problems

scholarly journals Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model

2017 ◽  
Vol 17 (3) ◽  
pp. 377-396 ◽  
Author(s):  
Trygve Bærland ◽  
Jeonghun J. Lee ◽  
Kent-Andre Mardal ◽  
Ragnar Winther
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Linear Elasticity ◽  
Discrete Systems ◽  
Model Parameters ◽  
Incompressible Limit ◽  
Biot Model ◽  
Finite Element Approximations ◽  
Consolidation Model ◽  
Biot’S Consolidation

AbstractWe discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are well-conditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.

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