A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
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V. Dhanya Varma
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
Funding source: Council of Scientific and Industrial Research (CSIR)
Award Identifier / Grant number: 09/874(0031)/2018/EMR-I
Acknowledgments
The authors would like to thank Council of Scientific and Industrial Research (CSIR), India (09/874(0031)/2018/EMR-I) for their support.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was funded by Council of Scientific and Industrial Research (CSIR).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Theorem A.1
Let E be a triangle or parallelogram in two dimension or a tetrahedron or hexahedron in three dimension. Let v ∈ H
s
(E) for s ≥ 1. Let k ≥ 0 be an integer. There exist a constant C independent of v and h
E
and a function
Lemma A.2
(Gronwall’s inequality). Let f, g, h be piecewise continuous non-negative functions defined on (a, b). Assume that g is nondecreasing. Assume that there is a positive constant C independent of t such that
Then,
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Coordinated target tracking in sensor networks by maximizing mutual information
- Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
- Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
- Extended logistic map for encryption of digital images
- Valuation of the American put option as a free boundary problem through a high-order difference scheme
- Power minimization of gas transmission network in fully transient state using metaheuristic methods
- A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
- Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
- Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
- New insights into singularity analysis
- Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
- Wavelet collocation methods for solving neutral delay differential equations
- Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
- Solving nonlinear third-order boundary value problems based-on boundary shape functions
- Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
- Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
- A fractional-order ship power system: chaos and its dynamical properties
- Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
- Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
- Modelling and numerical synchronization of chaotic system with fractional-order operator
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Coordinated target tracking in sensor networks by maximizing mutual information
- Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
- Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
- Extended logistic map for encryption of digital images
- Valuation of the American put option as a free boundary problem through a high-order difference scheme
- Power minimization of gas transmission network in fully transient state using metaheuristic methods
- A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
- Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
- Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
- New insights into singularity analysis
- Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
- Wavelet collocation methods for solving neutral delay differential equations
- Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
- Solving nonlinear third-order boundary value problems based-on boundary shape functions
- Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
- Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
- A fractional-order ship power system: chaos and its dynamical properties
- Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
- Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
- Modelling and numerical synchronization of chaotic system with fractional-order operator
