Analysis of polynomial interpolation of the function of two variables with large gradients in the parabolic boundary layers

2016 ◽  
Author(s):  
S. V. Tikhovskaya ◽  
A. I. Zadorin
Keyword(s):  
Boundary Layers ◽  
Polynomial Interpolation ◽  
Parabolic Boundary ◽  
Function Of Two Variables ◽  
Parabolic Boundary Layers

Some comments on a singular elliptic problem associated with a rectangle

1979 ◽  
Vol 83 (3-4) ◽  
pp. 283-296 ◽  
Author(s):  
V. A. Nye
Keyword(s):  
Approximate Solution ◽  
Boundary Layers ◽  
Elliptic Problem ◽  
Boundary Data ◽  
Correction Term ◽  
Parabolic Boundary ◽  
Parabolic Boundary Layers

SynopsisThe construction of the approximate solution within a rectangle of a singular elliptic problem is discussed. It is found that, provided the boundary data satisfy certain continuity conditions at the corners of the rectangle, ordinary boundary layers and parabolic boundary layers only are necessary to describe the solution. A correction term, however, has to be added to the solution if the continuity conditions on the boundary data are not satisfied.

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