The Best-Approximation Weighted-Residuals method for the steady convection-diffusion-reaction problem

2011 ◽  
Vol 82 (1) ◽  
pp. 144-162 ◽  
Author(s):  
G. Deolmi ◽  
F. Marcuzzi ◽  
M. Morandi Cecchi
Keyword(s):  
Best Approximation ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Weighted Residuals ◽  
The Best Approximation ◽  
Steady Convection ◽  
Reaction Problem

scholarly journals A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2524
Author(s):  
Fengxin Sun ◽  
Jufeng Wang ◽  
Xiang Kong ◽  
Rongjun Cheng
Keyword(s):  
Numerical Solutions ◽  
Splitting Method ◽  
Singularly Perturbed ◽  
Diffusion Reaction ◽  
Element Free Galerkin Method ◽  
Convection Diffusion ◽  
Discrete Equations ◽  
Element Free Galerkin ◽  
Element Free ◽  
Steady Convection

By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.

scholarly journals Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem

2021 ◽  
Author(s):  
Toni Sayah ◽  
Georges Semaan ◽  
Faouzi Triki
Keyword(s):  
Finite Element ◽  
Numerical Scheme ◽  
A Priori ◽  
Diffusion Reaction ◽  
The Finite Element Method ◽  
Existence Of A Solution ◽  
A Priori Error Estimate ◽  
Convection Diffusion ◽  
Reaction Problem ◽  
Theoretical Accuracy

In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm  the theoretical accuracy of the discretization.

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.

scholarly journals Error Estimates for the Heterogeneous Multiscale Finite Volume Method of Convection-Diffusion-Reaction Problem

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Tao Yu ◽  
Peichang Ouyang ◽  
Haitao Cao
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Diffusion Reaction ◽  
Optimal Order ◽  
Convection Diffusion ◽  
Heterogeneous Multiscale ◽  
Multiscale Finite Volume ◽  
Volume Method ◽  
Optimal Order Convergence ◽  
Reaction Problem

Based on the heterogeneous multiscale method, this paper presents a finite volume method to solve multiscale convection-diffusion-reaction problem. The paper constructs an algorithm of the optimal order convergence rate in H1-norm under periodic medias.

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