Numerical Analysis of Convection‐Diffusion‐Reaction Problems with Higher Order Characteristics/Finite Elements. Part I: Time Discretization

2006 ◽  
Vol 44 (5) ◽  
pp. 1829-1853 ◽  
Author(s):  
Alfredo Bermúdez ◽  
Maria R. Nogueiras ◽  
Carlos Vázquez
Keyword(s):  
Numerical Analysis ◽  
Finite Elements ◽  
Time Discretization ◽  
Higher Order ◽  
Diffusion Reaction ◽  
Convection Diffusion

scholarly journals A systematic approach to reduced GLT

2021 ◽  
Author(s):  
Giovanni Barbarino
Keyword(s):  
Spectral Analysis ◽  
Finite Elements ◽  
Differential Equations ◽  
Measurable Function ◽  
Finite Differences ◽  
Numerical Approximation ◽  
Systematic Approach ◽  
Diffusion Reaction ◽  
Full Detail ◽  
Convection Diffusion

AbstractThis paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations, in case the domain is a generic Peano–Jordan measurable set. It is observed that such matrix-sequences often present a spectral symbol, that is a measurable function describing the asymptotic behaviour of the eigenvalues. When the domain is a hypercube, the analysis can be conducted using the theory of generalized locally Toeplitz (GLT) sequences, but in case of generic domains, a different kind of matrix-sequences and theory has to be formalized. We thus develop in full detail the theory of reduced GLT sequences and symbols, presenting some application to finite differences and finite elements discretization for linear convection–diffusion–reaction differential equations.

Numerical Analysis of Inverse Problems for the Model of Transfer of Industrial Environmental Pollution in the Machine-Building

2015 ◽  
Vol 770 ◽  
pp. 695-700
Author(s):  
O.V. Soboleva
Keyword(s):  
Numerical Analysis ◽  
Inverse Problems ◽  
Environmental Pollution ◽  
Numerical Experiments ◽  
Extremum Problem ◽  
Machine Building ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Specific Cost ◽  
Convection Diffusion

The model of transfer of polluting substance is considered. Inverse extremum problem of identification of the coefficients in an elliptic convection-diffusion-reaction equation is formulated. The solvability of this problem is proved and the optimality system is constructed for specific cost functional. The numerical algorithm based on Newton-method of nonlinear optimization of linear elliptic problems is developed and programmed on computer. The results of numerical experiments are presented. Influence of coefficient of convection on stability of algorithm of the solution of the inverse extremum problem is investigated.

scholarly journals Robust Numerical Methods for Singularly Perturbed Differential Equations: A Survey Covering 2008–2012

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Hans-Görg Roos
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Differential Equations ◽  
Adaptive Methods ◽  
Singularly Perturbed ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Stabilization Methods ◽  
Singularly Perturbed Equations

We present new results in the numerical analysis of singularly perturbed convection-diffusion-reaction problems that have appeared in the last five years. Mainly discussing layer-adapted meshes, we present also a survey on stabilization methods, adaptive methods, and on systems of singularly perturbed equations.

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