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 co...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 epsilon-uniform in the sense that the Fate of convergence and error constant of the method are independent of the singular perturbation parameter epsilon. This means that no matter how small the singular perturbation parameter epsilon is, the numerical method produces solutions with guaranteed accuracy depending solely on the number of mesh points used.展开更多
文摘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 epsilon-uniform in the sense that the Fate of convergence and error constant of the method are independent of the singular perturbation parameter epsilon. This means that no matter how small the singular perturbation parameter epsilon is, the numerical method produces solutions with guaranteed accuracy depending solely on the number of mesh points used.
