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 -

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.