Numerical Solution of a Singularly Perturbed Problem on a Circular Domain - A. F. Hegarty; E. O’Riordan (Моделирование и анализ информационных систем, 2016)
We consider a singularly perturbed elliptic problem, of convection-diﬀusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-uniform under certain compatibility constraints. Numerical results are presented to illustrate the performance of the numerical method when these constraints are not imposed on the data.