Superconvergence in the generalized finite element method

In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions, and was developed in (Babuška et al. in SIAM J Numer Anal 31, 945–981, 1994; Babuška et al. in Int J Numer Meth Eng 40, 727–758, 1997; Melenk and Babuška in Comput Methods Appl Mech Eng 139, 289–314, 1996). In particular, we show that the superconvergence points for the gradient of the approximate solution are the zeros of a system of non-linear equations; this system does not depend on the solution of the boundary value problem. For approximate solutions with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate solution as the roots of a system of non-linear equations. We note that smooth generalized finite element approximation is easy to construct. I. Babuška’s research was partially supported by NSF Grant # DMS-0341982 and ONR Grant # N00014-99-1-0724. U. Banerjee’s research was partially supported by NSF Grant # DMS-0341899. J. E. Osborn’s research was supported by NSF Grant # DMS-0341982.     

Anwendung der Röntgenspektrographie für die Untersuchung kolloider Systeme

Ohne Zusammenfassung     

Ueber die Reifung der Viskose

Ohne Zusammenfassung     

Effect of capillary cross-section geometry and size on the separation of proteins in gradient mode using monolithic poly(butyl methacrylate-co-ethylene dimethacrylate) columns

Porous polymer monoliths have been prepared in capillaries with circular or square cross-sections and lateral dimensions of 50, 75, 100 μm as well as in a rectangular 38 μm × 95 μm capillary. These capillaries have been used to determine the effect of the size and shape of their cross-section on the porous and hydrodynamic properties of poly(butyl methacrylate-co-ethylene dimethacrylate) monoliths. The capillaries were studied by scanning electron microscopy and evaluated for their permeability to flow and their performance in the liquid chromatographic separation of a protein mixture comprising ribonuclease A, cytochrome c, myoglobin, and ovalbumin using a linear gradient of acetonitrile in the mobile phase. No differences resulting from channel geometry were found for the various capillary columns. These results demonstrate that standard capillaries with circular geometry are a good and affordable alternative conduit for modeling the processes carried out in microfluidic chips with a variety of geometries.