A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.     

Visible Light Mediated Halogen Atom Transfer to Access Polyhalogenated and Deuterated Lactams from Alkyl Halides

A visible light mediated protocol for the synthesis of polyhalogenated and deuterated δ- and γ-lactams from readily available alkyl halides is reported. The reaction involves the generation of haloalkyl radicals through halogen atom transfer (XAT) and subsequent arylalkylation of olefins to afford dihydroisoquinolinones and oxindoles. This new XAT protocol exhibits wide scope under mild conditions and enables access to new halogenated chemical space.     

Iron‐Catalyzed C(sp2)H and C(sp3)H Methylations of Amides and Anilides

The so‐called magic methyl effect significantly boosts the bioactivities and physical properties of pharmacologically active drugs. Direct introduction of the methyl group by C?H activation was accomplished with a versatile iron catalyst, which enabled the C?H methylation of (hetero)benzamides, anilides, alkenes, and even alkanes by triazole assistance in a chemo‐, site‐ and diastereo‐selective fashion.     

Metal‐Catalyzed “On‐Demand” Production of Carbonyl Sulfide from Carbon Monoxide and Elemental Sulfur

The group 6 molybdenum(II) cyclopentadienyl amidinate (CPAM) bis(carbonyl) complex [Cp*Mo{N(iPr)C(Ph)N(iPr)}(CO)₂] (Cp*=η⁵‐C₅Me₅) serves as a precatalyst for the high‐yielding photocatalytic production of COS from CO and S₈ under near‐ambient conditions (e.g., 10 psi, 25 °C). Further documented is the isolation and structural characterization of several key transition‐metal intermediates which collectively support a novel molybdenum(IV)‐based catalytic cycle as being operative. Finally, in the presence of an excess amount of a primary amine, it is demonstrated that this catalytic system can be successfully used for the “on‐demand” generation and utilization of COS as a chemical reagent for the synthesis of ureas.     

Observation of Diastereotopic Signals in 15N NMR Spectroscopy

The first example in the literature of a compound showing anisochronous ¹⁵N atoms resulting from diastereotopicity is described. Racemic 1,3‐dimethyl‐2‐phenyloctahydro‐1H‐benzimidazole was prepared and studied by ¹H, ¹³C and ¹⁵N NMR spectroscopy. If convenient conditions were used (monitored by theoretical calculations of ²J_N‐H spin–spin coupling constants), two ¹⁵N NMR signals were observed and corresponded to the diastereotopic atoms. GIAO/density‐functional calculations of chemical shifts were not only in good agreement with the experimental values but also served as prediction tools. This study suggests that ¹⁵N NMR spectroscopy could be used to probe chirality.     

A General and Scalable Synthesis of Aeruginosin Marine Natural Products Based on Two Strategic C(sp3)H Activation Reactions

An efficient and scalable access to the aeruginosin family of marine natural products, which exhibit potent inhibitory activity against serine proteases, is reported. This synthesis was enabled by the strategic use of two different, recently implemented C(sp³)? H activation reactions. The first method led to the common 2‐carboxy‐6‐hydroxyoctahydroindole (Choi) core of the target molecules on a large scale, whereas the second one provided rapid and divergent access to the various hydroxyphenyllactic (Hpla) subunits. This strategy allowed the synthesis of the aeruginosins 98B and 298A, with the latter being obtained in unprecedentedly large quantities.     

O2‐mediated dehydrogenative amination of phenols

A method was developed for the direct dehydrogenative construction of C? N bonds between unprotected phenols and a series of cyclic anilines without resorting to any kind of metal activation of either substrate and without the use of halides. The resulting process relies on the exclusively organic activation of molecular oxygen and the subsequent oxidation of the aniline substrate. This allows the coupling of ubiquitous phenols, thus furnishing aminophenols through an atom‐economical and most sustainable dehydrogenative amination method. This new reactivity, which relies on the intrinsic organic reactivity of cumene in what can be seen as a modified Hock activation process of oxygen, is expected to have a large impact on the formation of C? N bonds in organic synthesis.     

Gold(I)‐Catalyzed Tandem Transformation with Diynes: Rapid Access to Linear Cyclopentenone‐Fused Polycyclic Molecules

An efficient and convenient synthesis of useful linear cyclopentenone‐fused polycyclic compounds has been achieved through a novel gold(I)‐catalyzed transformation of diynes. The method demonstrates high product yields and tolerates of a wide variety of important functional groups. Gold‐vinylidene formation, methoxy group migration, and Nazarov‐type cyclization are proposed to be the key steps in the reaction pathway. The synthetic utility of this method is demonstrated by converting the product to eight‐membered‐ring‐fused compound.