scholarly journals A posteriori error estimates for non-stationary non-linear convection–diffusion equations

CALCOLO ◽  
2018 ◽  
Vol 55 (2) ◽  
Author(s):  
R. Verfürth
Keyword(s):  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Diffusion Equations ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Convection Diffusion ◽  
Non Linear

scholarly journals A Posteriori Error Estimates for Hughes Stabilized SUPG Technique and Adaptive Refinement for a Convection-Diffusion Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Brehmit Kaur ◽  
Vivek Sangwan
Keyword(s):  
Singular Perturbation ◽  
Boundary Layers ◽  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Perturbation Parameter ◽  
Diffusion Problem ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Convection Diffusion

The motive of the present work is to propose an adaptive numerical technique for singularly perturbed convection-diffusion problem in two dimensions. It has been observed that for small singular perturbation parameter, the problem under consideration displays sharp interior or boundary layers in the solution which cannot be captured by standard numerical techniques. In the present work, Hughes stabilization strategy along with the streamline upwind/Petrov-Galerkin (SUPG) method has been proposed to capture these boundary layers. Reliable a posteriori error estimates in energy norm on anisotropic meshes have been developed for the proposed scheme. But these estimates prove to be dependent on the singular perturbation parameter. Therefore, to overcome the difficulty of oscillations in the solution, an efficient adaptive mesh refinement algorithm has been proposed. Numerical experiments have been performed to test the efficiency of the proposed algorithm.

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