On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

2017 ◽  
Vol 60 (3) ◽  
pp. 479-492 ◽  
Author(s):  
Jörg Schröder ◽  
Nils Viebahn ◽  
Peter Wriggers ◽  
Ferdinando Auricchio ◽  
Karl Steeger
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Boundary Value Problems ◽  
Mixed Finite Element ◽  
Boundary Value ◽  
The Stability ◽  
Finite Element Formulations

scholarly journals Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect

2020 ◽  
Vol 75 ◽  
pp. 33
Author(s):  
Mohamed F. El-Amin ◽  
Jisheng Kou ◽  
Shuyu Sun
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Shale Gas ◽  
Gas Flow ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Model ◽  
Mathematical Proofs ◽  
The Stability ◽  
Shale Gas Transport

In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

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.

scholarly journals On the Stability of Mixed Finite-Element Formulations for High-Temperature Superconductors

2021 ◽  
pp. 1-1
Author(s):  
Julien Dular ◽  
Mane Harutyunyan ◽  
Lorenzo Bortot ◽  
Sebastian Schops ◽  
Benoit Vanderheyden ◽  
...  
Keyword(s):  
Finite Element ◽  
High Temperature ◽  
Mixed Finite Element ◽  
High Temperature Superconductors ◽  
The Stability ◽  
Finite Element Formulations
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