Error Analysis of an Extended Discontinuous Galerkin (XDG) Scheme for Boundary Layer Problems

şuayip toprakseven, Donald French, Benjamin VAUGHAN

Abstract


We investigate an extended discontinuous Galerkin (XDG) method for boundary
layer problems in this paper.
This scheme is formed by introducing special boundary layer functions into
standard Discontinuous Galerkin (DG) approximation spaces.
Error estimates in a special energy norm and the $L^2$ norm are provided
for this XDG scheme.
We also demonstrate the performance of this the XDG scheme through sample
computations. The theory and numerics suggest this approach is more accurate that standard
approaches.


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