Discontinuous Galerkin finite volume element methods for second‐order linear elliptic problems

In this article, a one parameter family of discontinuous Galerkin finite volume element methods for approximating the solution of a class of second‐order linear elliptic problems is discussed. Optimal error estimates in L² and broken H¹‐ norms are derived. Numerical results confirm the theoretical order of convergences. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

QSAR analysis of 1,3-diaryl-2-propen-1-ones and their indole analogs for designing potent antibacterial agents

A series of 1,3-diaryl-2-propen-1-ones and their indole analogs were synthesized and evaluated for antibacterial activity. Structures of newly synthesized compounds were confirmed by physicochemical, spectral and elemental analysis. All the compounds were screened for their antibacterial activities against four different bacterial strains. The QSAR studies were performed using Vlife MDS 3.5 software. QSAR equation revealed that selected electronic, steric and lipophilic parameters have good correlation with antibacterial activity. Best equations were selected on basis of the correlation coefficient (r ²) and the predictable ability of the equations. The present findings suggest that the 1,3-diaryl-2-propen-1-ones framework is an attractive template for structure optimization to achieve higher potency, lower toxicity, and a wider spectrum of antibacterial activity.     

A simple, convenient method for the synthesis of maleic anhydrides from α-keto esters and alkanoic acid anhydrides using the TiCl4/n-Bu3N reagent system

Reaction of α-keto esters with alkanoic acid anhydrides using the TiCl₄/n-Bu₃N reagent system gives the corresponding maleic anhydrides in 62-95% yields.     

Analyzing coordination preferences of Mg2+ complexes: insights from computational and database study

Solvation of metal cations has attracted substantial interest on account of its functional importance in biological systems. In the present study, we undertake a comprehensive analysis of hydrated complexes of Mg²⁺ with up to 20 water molecules using MP2/cc-pVTZ and density functional theory (DFT) calculations. The effect of first, second, and higher solvation shells on magnesium coordination has been systematically analyzed by considering Mg²⁺(H₂O) _n complexes. Numerous competing conformations for each of the metal ion complexes have been explored and the minima structures obtained were further analyzed. The study probes the relative preferences among various coordination numbers and unambiguously establishes that coordination number 6 is the most optimal choice. The relative abundance of Mg²⁺ ion and its coordination with water and other ligands has been analyzed in the Protein Data Bank and Cambridge Structural Database. It is noted that the M–O distance and charge transfer to metal ion increase as the number of solvating water molecules increases. The computational studies are in excellent agreement with the experimental observations, and provide support to multiple coordinate site preferences for Mg²⁺.     

Double-diffusive convection with fine dust

The effect of fine dust (suspended particles) is considered on the thermosolutal convection. The principle of exchange of stabilities is satisfied for thermal Rayleigh number greater than or equal to solute Rayleigh number. If the solute Rayleigh number exceeds the thermal Rayleigh number, the oscillatory modes may come into play. The effect of stable solute gradient has a stabilizing effect whereas the effect of suspended particles is to destabilize the layer. The effect of a uniform rotation is also considered and is found to have a stabilizing effect in the presence of suspended particles on the thermosolutal convection.     

Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow

Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L^∞( L ²) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L^∞( L ²) as well as in L^∞( H )‐norms and the pressure in L^∞(L²)‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Thermal convection problem of micropolar fluid subjected to hall current

Thermal instability of a micropolar fluid layer heated from below in the presence of hall currents is investigated. Using the appropriate boundary conditions on the boundary surfaces of the fluid layer, the frequency equation is derived and then critical Rayleigh number is determined. It is found that hall current parameter has destabilizing effect on the system. For specific values of parameters, oscillatory convection in observed in the system. The behavior of Rayleigh number with wavenumber is also computed for different values of various parameters. The results of some earlier workers have been reduced as a special case from the present problem.     

A posteriori error estimates for an optimal control problem of laser surface hardening of steel

The main focus of this article is on the development of a posteriori error estimates for an optimal control problem of laser surface hardening of steel, governed by a dynamical system consisting of a semi-linear parabolic equation and an ordinary differential equation. A posteriori error estimators are developed for the variables representing temperature, formation of austenite, and laser energy using residual method when a continuous piecewise linear discretization has been used for the finite element approximation of space variables and a discontinuous Galerkin method has been used for time and control discretizations. The error indicators are used in the implementation and numerical results are obtained.     

A new mixed finite element method for Burgers’ equation

In this paper, anH ¹-Galerkin mixed finite element method is used to approximate the solution as well as the flux of Burgers’ equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.     

A mixed finite element method for fourth order eigenvalue problems

A mixed finite element method for approximating eigenpairs of IV order elliptic eigenvalue problems with Dirichlet boundary conditions has been given. The method can be applied to the vibration analysis of anisotropic/orthotropic/isotropic/biharmonic plates. Computer implementation procedures for this mixed method are given along with the results of numerical experiments.