Interior and superconvergence estimates for mixed methods for second order elliptic problems

Efficient rectangular mixed finite elements in two and three space variables

“…The interior estimâtes derived by Douglas and Milner [13] for the Raviart-Thomas spaces, as the global estimâtes, depended only on the properties of the projection U h x Q h ; hence, the corresponding estimâtes hold for the new éléments. Let G be an open subset of H, and set…”

“…note that the boundary values g are not involved in the équations for an interior solution, since supp (|x) a G. The following theorem is analogous to Theorem 2.2 of [13]. The négative norm estimâtes of this theorem and an analogous one for différence quotients, corresponding to Theorem 4.1 of [13] when the décomposition has a translation invariance over an interior subdomain can be used to dérive superconvergence via Bramble-Schatz postprocessing of the approximate solution.…”

“…See [13,16] for such extensions. Some of the discussion of the algebraic équations associated with (1.4) would require modification to handle the gênerai case.…”

Local error estimates for finite element discretization of the Stokes equations

“…See Wahlbin's handbook article [12,ChapterlII] for an extensive treatment. In 1985 Douglas and Milner adapted the Nitsche-Schatz approach to the Raviart-Thomas mixed method for scalar second order elliptic problems [5], The present work adapts it to analyze a wide class of methods for the Stokes équations. Although the gênerai approach is not new, there are a number of significant difficulties which anse for the Stokes System that are not present in previous works.…”

Superconvergence for Control‐Volume Mixed Finite Element Methods on Rectangular Grids

“…A number of authors have studied superconvergence for the above method or the closely related CCFD method [25,14,29,15,16,18,4] and have shown results of the form…”