A Posteriori Error Estimates for Non-Stationary Non-Linear Convection-Diffusion Equations
It provides error estimation for a class of PDEs that do not fit standard frameworks, benefiting researchers in numerical analysis and stochastic PDEs.
The paper derives a posteriori error estimates for non-stationary non-linear convection-diffusion equations, addressing a deterministic paradigm for stochastic problems. The estimates account for the interplay of parameters controlling diffusion, convection, reaction, and non-linearity.
Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the standard linear framework due to its non-linearity nor into the standard non-linear framework due to the lacking differentiability of the non-linearity. Particular attention is paid to the interplay of the various parameters controlling the relative sizes of diffusion, convection, reaction, and non-linearity (noise).