Stability Analysis of the ALE-STDGM for Linear Convection-Diffusion-Reaction Problems in Time-Dependent Domains

2016 ◽  
pp. 215-223
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer
Keyword(s):  
Stability Analysis ◽  
Time Dependent ◽  
Diffusion Reaction ◽  
Convection Diffusion

scholarly journals Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

2020 ◽  
Vol 84 ◽  
pp. 425-446
Author(s):  
Luis Miguel De Oliveira Vilaca ◽  
Bryan Gómez-Vargas ◽  
Sarvesh Kumar ◽  
Ricardo Ruiz-Baier ◽  
Nitesh Verma
Keyword(s):  
Stability Analysis ◽  
Diffusion Reaction ◽  
New Model ◽  
Convection Diffusion

scholarly journals Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Jen-Yi Chang ◽  
Ru-Yun Chen ◽  
Chia-Cheng Tsai
Keyword(s):  
Shape Parameter ◽  
Source Term ◽  
Time Dependent ◽  
Diffusion Reaction ◽  
System Matrix ◽  
Time Step ◽  
Convection Diffusion ◽  
Particular Solutions ◽  
Particular Solution ◽  
Reaction Problem

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

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