Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

We present a new approach to enforcing local maximum principles in finite element schemes for the compressible Euler equations. In contrast to synchronized limiting techniques for systems of conservation laws, the density, momentum, and total energy are constrained in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum are adjusted to incorporate the irreversible effect of density changes. Then the corresponding antidiffusive corrections are limited to satisfy inequality constraints for the total and kinetic energy. The same element-based limiting strategy is employed in the context of continuous and discontinuous Galerkin methods. The sequential nature of the new limiting procedure makes it possible to achieve crisp resolution of contact discontinuities while using sharp local bounds in the energy constraints. A numerical study is performed for piecewise-linear finite element discretizations of 1D and 2D test problems

Effects of TLR Agonists on the Hypoxia-Regulated Transcription Factor HIF-1α and Dendritic Cell Maturation under Normoxic Conditions

Dendritic cells (DC) are professional antigen presenting cells that represent an important link between innate and adaptive immunity. Danger signals such as toll-like receptor (TLR) agonists induce maturation of DC leading to a T-cell mediated adaptive immune response. In this study, we show that exogenous as well as endogenous inflammatory stimuli for TLR4 and TLR2 induce the expression of HIF-1α in human monocyte-derived DC under normoxic conditions. On the functional level, inhibition of HIF-1α using chetomin (CTM), YC-1 and digoxin lead to no consistent effect on MoDC maturation, or cytokine secretion despite having the common effect of blocking HIF-1α stabilization or activity through different mechanisms. Stabilization of HIF-1α protein by hypoxia or CoCl2 did not result in maturation of human DC. In addition, we could show that TLR stimulation resulted in an increase of HIF-1α controlled VEGF secretion. These results show that stimulation of human MoDC with exogenous as well as endogenous TLR agonists induces the expression of HIF-1α in a time-dependent manner. Hypoxia alone does not induce maturation of DC, but is able to augment maturation after TLR ligation. Current evidence suggests that different target genes may be affected by HIF-1α under normoxic conditions with physiological roles that differ from those induced by hypoxia