A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

2-(4-Amino-3-methylphenyl)-5-fluorobenzothiazole is a ligand and shows species-specific partial agonism of the Aryl Hydrocarbon Receptor

2-(4-Amino-3-methylphenyl)-5-fluorobenzothiazole (5F 203) and related compounds are a series of anti-cancer candidate pharmaceuticals (Table 1.), that have been shown to activate the AhR. We show that these compounds are high affinity ligands for the rat AhR, but a quantitative assay for their ability to induce CYP1A1 RNA in H4IIEC3 cells, a measure of activation of the AhR, showed a poor relationship between affinity for the AhR and ability to induce CYP1A1 RNA. 5F 203, an agonist with low potency, was able to antagonise the induction of CYP1A1 RNA by TCDD, while IH 445, a potent agonist, did not antagonise the induction of CYP1A1 RNA by TCDD, and Schild analysis confirmed 5F 203 to be a potent antagonist of the induction of CYP1A1 RNA by TCDD in H4IIEC3 cells. In contrast, several benzothiazoles show potent induction of CYP1A1 RNA in human MCF-7 cells, and 5F 203 is unable to detectably antagonise the induction of CYP1A1 RNA in MCF-7 cells, showing a species difference in antagonism. Evaluation of the antiproliferative activity of benzothiazoles showed that the ability to agonise the AhR correlated with growth inhibition both in H4IIEC3 cells for a variety of benzothiazoles, and between H4IIEC3 and MCF-7 cells for 5F 203, suggesting an important role of agonism of the AhR in the anti-proliferative activity of benzothiazoles.