A note on convergence of line iterative methods for a nine-point matrix
The authors consider the special convection-diffusion equation, \(-\varepsilon\Delta u+u_x=f\), with unit convection velocity parallel to the \(x\)-coordinate direction. The domain of interest is the unit square and the equation is discretized with uniform square mesh elements with side length \(h\). The critical parameter is the so-called cell Reynolds number \(\gamma=h/(2\varepsilon)\). The authors employ a fourth order difference scheme due to \textit{M. M. Gupta, R. P. Manohar} and \textit{J. W. Stephenson} [Numerical properties and methodologies in heat transfer, Proc. 2nd nat. Symp., College Park, Md. 1981, 201-209 (1983; Zbl 0515.76097)].
scientific article; zbMATH DE number 1878880
scientific article