Higher-order finite element methods for elliptic problems with interfaces

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.Comment: 26 pages, 6 figures. An earlier version of this paper appeared on November 13, 2014 in http://www.brown.edu/research/projects/scientific-computing/reports/201

Study of the pore structure of ceramics prepared by the slip casting method

The porosity of the slip cast Si3N4 is similar to that of pressed Si3N4 formed at 2500 kg/sq cm. The porosity of cast Si oxynitride is equivalent to that of samples stressed at 10,000 kg/sq cm. Crucibles formed from these materials by slip casting have high thermal shock and corrosion resistance