A Posteriori Error Estimates for Non-Stationary Non-Linear Convection-Diffusion Equations

2018/02/06 by Verfürth, Rüdiger
#65J10 #65N15 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1802.02453

Abstract

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).

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