scholarly journals Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity

2021 ◽  
Author(s):  
Manu Jayadharan ◽  
Eldar Khattatov ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Mixed Finite Element ◽  
Partitioning Methods ◽  
Finite Element Discretizations ◽  
Biot System ◽  
Element Discretizations

scholarly journals ON THE INF–SUP CONDITION OF MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUIDS

2001 ◽  
Vol 11 (05) ◽  
pp. 883-901 ◽  
Author(s):  
WEIZHU BAO ◽  
XIAODONG WANG ◽  
KLAUS-JÜRGEN BATHE
Keyword(s):  
Finite Element ◽  
Error Bounds ◽  
Natural Frequencies ◽  
Mixed Finite Element ◽  
Optimal Error ◽  
Finite Element Discretizations ◽  
Analytical Proof ◽  
The Stability ◽  
Element Discretizations ◽  
Finite Element Formulations

The objective of this paper is to present a study of the solvability, stability and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is given, and the interrelationship between the inf–sup condition, including the numerical inf–sup test, and the eigenvalue problem pertaining to the natural frequencies is discussed.

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