Title: Robust consistent a posteriori error majorants for approximate solutions of diffusion-reaction equations,
Abstract: Efficiency of the error control of numerical solutions of partial
differential equations entirely depends on the two factors: accuracy of an a
posteriori error majorant and the computational cost of its evaluation for some
test function/vector-function plus the cost of the latter. In the paper,
consistency of an a posteriori bound implies that it is the same in the order
with the respective unimprovable a priori bound. Therefore, it is the basic
characteristic related to the first factor. The paper is dedicated to the
elliptic diffusion-reaction equations. We present a guaranteed robust a
posteriori error majorant effective at any nonnegative constant reaction
coefficient (r.c.). For a wide range of finite element solutions on a
quasiuniform meshes the majorant is consistent. For big values of r.c. the
majorant coincides with the majorant of Aubin (1972), which, as it is known,
for not big r.c. ($<ch^{-2}$) is inconsistent and loses its sense at r.c.
approaching zero. Our majorant improves also some other majorants derived for
the Poisson and reaction-diffusion equations.