Order Reduction and Uniform Convergence of an Alternating Direction Method for Solving 2D Time Dependent Convection-Diffusion Problems

2017 ◽  
pp. 49-61
Author(s):  
C. Clavero ◽  
J. C. Jorge
Keyword(s):  
Uniform Convergence ◽  
Order Reduction ◽  
Alternating Direction Method ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Alternating Direction ◽  
Diffusion Problems

An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems

2016 ◽  
Vol 20 (5) ◽  
pp. 1340-1358 ◽  
Author(s):  
Yanping Chen ◽  
Li-Bin Liu
Keyword(s):  
Numerical Solution ◽  
Time Derivative ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Time Dependent ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Monitor Function ◽  
Backward Euler ◽  
Diffusion Problems

AbstractIn this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε-uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.

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