TY - JOUR
T1 - Pointwise Approximation of Corner Singularities for Singularly Perturbed Elliptic Problems with Characteristic Layers
AU - V. B. Andreev
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 416
EP - 427
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/728.html
KW - Parabolic boundary layers, elliptic equation, piecewise uniform mesh, corner singularities.
AB - <p style="text-align: justify;">A Dirichlet problem for a singularly perturbed steady-state convection-diffusion equation with constant coefficients on the unit square is considered.
In the equation under consideration the convection term is represented
by only a single derivative with respect to one coordinate axis. This problem is
discretized by the classical five-point upwind difference scheme on a rectangular
piecewise uniform mesh that is refined in the neighborhood of the regular and
the characteristic boundary layers. It is proved that, for sufficiently smooth
right-hand side of the equation and the restrictions of the continuous boundary
function to the sides of the square, without additional compatibility conditions
at the corners, the error of the discrete solution is $O(N^{-1}\ln^2 N)$ uniformly
with respect to the small parameter, in the discrete maximum norm, where $N$ is the number of mesh points in each coordinate direction.</p>