The norm of a discretized gradient in $$\varvec{H({{\mathrm{div}}})^*}$$ H ( div ) ∗ for a posteriori finite element error analysis

Abstract

This paper characterizes the norm of the residual of mixed schemes in their natural functional framework with fluxes or stresses in \(H({{\mathrm{div}}})\) and displacements in \(L^2\). Under some natural conditions on an associated Fortin interpolation operator, reliable and efficient error estimates are introduced that circumvent the duality technique and so do not suffer from reduced elliptic regularity for non-convex domains. For the Laplace, Stokes, and Lamé equations, this generalizes known estimators to non-convex domains and introduces new a posteriori error estimators.