Multilevel a posteriori error analysis for reaction-convection-diffusion problems (Q1878388)

Considering a variational formulation of the exact problem based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales, a new approach to a posteriori error analysis of the finite dimensional approximation of reaction-convection-diffusion problem is presented. Although the results are obtained in a very specific situation, they indicate new directions [cf. \textit{A. Cohen, W. Dahmen} and \textit{R. DeVore}, Found. Comput. Math. 2, 203--245 (2002; Zbl 1025.65056)].