Error-controlled adaptive mixed finite element methods for second-order elliptic equations

摘要

In this contribution, we deal with a posteriori error estimates and adaptivity for mixed finite element discretizations of second-order elliptic equations, which are applied to the Poisson equation. The method proposed is an extension to the one recently introduced in [10] to the case of inhomogeneous Dirichlet and Neumann boundary conditions. The residual-type a posteriori error estimator presented in this paper relies on a postprocessed and therefore improved solution for the displacement field which can be computed locally, i.e. on the element level. Furthermore, it is shown that this discontinuous postprocessed solution can be further improved by an averaging technique. With these improved solutions at hand, both upper and lower bounds on the finite element discretization error can be obtained. Emphasis is placed in this paper on the numerical examples that illustrate our theoretical results.