TY - JOUR
T1 - An Accurate Numerical Solution of a Two Dimensional Heat Transfer Problem with a Parabolic Boundary Layer
AU - Clavero , C.
AU - Miller , J.J.H.
AU - O'Riordan , E.
AU - Shishkin , G.I.
JO - Journal of Computational Mathematics
VL - 1
SP - 27
EP - 39
PY - 1998
DA - 1998/02
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9139.html
KW - Linear convection-diffusion, parabolic layer, piecewise uniform mesh, finite difference.
AB - <p style="text-align: justify;">A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically. The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numerically that the method is $ε$-uniform in the sense that the rate of convergence and error constant of the method are independent of the singular perturbation parameter $ε$. This means that no matter how small the singular perturbation parameter $ε$ is, the numerical method produces solutions with guaranteed accuracy depending solely on the number of mesh points used.&nbsp;</p>