A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.

Differential mechanisms of angiotensin II and PDGF-BB on migration and proliferation of coronary artery smooth muscle cells

Angiotensin II (Ang II) and platelet-derived growth factor-BB (PDGF-BB) are associated with excessive cell migration, proliferation and many growth-related diseases. However, whether these agents utilise similar mechanisms to trigger vascular pathologies remains to be explored. The effects of Ang II and PDGF-BB on coronary artery smooth muscle cell (CASMC) migration and proliferation were investigated via Dunn chemotaxis assay and the measurement of [3H]thymidine incorporation rates, respectively. Both atherogens produced similar degrees of cell migration which were dramatically inhibited by mevastatin (10 nM). However, the inhibitory effects of losartan (10 nM) and MnTBAP (a free radical scavenger; 50 μM) were found to be unique to Ang II-mediated chemotaxis. In contrast, MnTBAP, apocynin (an antioxidant and phagocytic NADPH oxidase inhibitor; 500 μM), mevastatin and pravastatin (100 nM) equally suppressed both Ang II and PDGF-BB-induced cellular growth. Although atherogens produced similar changes in NADPH oxidase, NOS and superoxide dismutase activities, they differentially regulated antioxidant glutathione peroxidase activity which was diminished by Ang II and unaffected by PDGF-BB. Studies with signal transduction pathway inhibitors revealed the involvement of multiple pathways i.e. protein kinase C, tyrosine kinase and MAPK in Ang II- and/or PDGF-BB-induced aforementioned enzyme activity changes. In conclusion, Ang II and PDGF-BB may induce coronary atherosclerotic disease formation by stimulating CASMC migration and proliferation through agent-specific regulation of oxidative status and utilisation of different signal transduction pathways.