Error estimation of numerical solutions of linear convection-diffusion problem

We present a new error estimating method of numerical solutions using the sensitivity analysis and modified equation techniques. The method can investigate not only the effects of numerical error but also those of uncertainty in a physical model at the same time. In this paper, we apply it to the finite-difference method of upwind and Lax-Wendroff schemes for the linear convection-diffusion problems. If a standard case of typical parameters is computed with the method, no additional computation is required to estimate the other numerical parameters' results such as more detailed solutions. Furthermore, we can quantitatively estimate the numerical error only from the sensitivity analysis results.