On the stability of finite-element discretizations of convection-diffusion-reaction equations

2009 ◽  
Vol 31 (1) ◽  
pp. 147-164 ◽  
Author(s):  
P. Knobloch ◽  
L. Tobiska
Keyword(s):  
Finite Element ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Finite Element Discretizations ◽  
The Stability ◽  
Reaction Equations ◽  
Element Discretizations

A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
V. Dhanya Varma ◽  
Suresh Kumar Nadupuri
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Fluidized Beds ◽  
A Priori ◽  
Coupled System ◽  
Diffusion Reaction ◽  
Strongly Coupled ◽  
Convection Diffusion ◽  
Finite Element Approximations ◽  
Reaction Equations

Abstract In this work, a priori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived. These equations are time dependent strongly coupled system of five semilinear convection-diffusion-reaction equations. The a priori error estimates for all the five variables are obtained for the error measured in L ∞(L 2) and L 2 ( E ) ${L}^{2}\left(\mathcal{E}\right)$ , E $\mathcal{E}$ is the energy norm.

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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