A Second-Order Difference Scheme for a Singularly Perturbed Reaction-Diffusion Problem

2013 ◽  
pp. 239-248 ◽  
Author(s):  
Basem S. Attili
Keyword(s):  
Difference Scheme ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Second Order ◽  
Singularly Perturbed ◽  
Order Difference

scholarly journals Singularly Perturbed Reaction–Diffusion Problems as First order systems

2021 ◽  
Vol 89 (2) ◽  
Author(s):  
Sebastian Franz
Keyword(s):  
Convergence Analysis ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Second Order ◽  
Singularly Perturbed ◽  
Convergence Order ◽  
First Order ◽  
Optimal Convergence ◽  
Balanced Norm ◽  
Diffusion Problems

AbstractWe consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $$H_{{{\,\mathrm{{div}}\,}}}$$ H div -conforming elements for the second component we provide a convergence analysis on layer adapted meshes and an optimal convergence order in a balanced norm that is comparable with a balanced $$H^2$$ H 2 -norm for the second order formulation.

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