Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's problem
In this study, we consider some recent stabilization techniques for the Stokes' problem and show that they are instances of the framework proposed by Brezzi and Fortin in "A minimal stabilisation procedure for mixed finite element methods" (Numer Math 89, (2001) 457). We also propose an analysis for Taylor-Hood elements with discontinuous pressures stabilized using penalization of the interelement pressure jumps. (c) 2007 Wiley Periodicals, Inc.
We describe preliminary results from an effort to quantify the uncertainties in parton distribution functions and the resulting uncertainties in predicted physical quantities. The production cross section of the $W$ boson is given as a first example. Constraints due to the full data sets of the CTEQ global analysis are used in this study. Two complementary approaches, based on the Hessian and the Lagrange multiplier method respectively, are outlined. We discuss issues on obtaining meaningful uncertainty estimates that include the effect of correlated experimental systematic uncertainties and illustrate them with detailed calculations using one set of precision DIS data.