A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems

Computable a posteriori error bounds and related adaptive mesh-refining alg orithms are provided for the numerical treatment of monotone stationary flo w problems with a quite general class of conforming and non-conforming fini te element methods. A refined residual-based error estimate generalises the works of Verfurth; Dari, Duran and Padra; Bao and Barrett. As a consequenc e, reliable and efficient averaging estimates can be established on unstruc tured grids. The symmetric formulation of the incompressible flow problem m odels certain nonNewtonian flow problems and the Stokes problem with mixed boundary conditions. A Helmholtz decomposition avoids any regularity or sat uration assumption in the mathematical error analysis. Numerical experiment s for the partly nonconforming method analysed by Kouhia and Stenberg indic ate efficiency of related adaptive mesh-refining algorithms.