In this article, we present a finite element scheme combined with backward Euler method to solve a nonlocal parabolic problem. An important issue in the numerical solution of nonlocal problems while using Newton's method is related to its structure. In fact differently from the local case where the Jacobian matrix is sparse and banded, in the nonlocal case the Jacobian matrix is dense and computations are much more onerous compared to that for differential equations. In order to avoid this difficulty, we use the technique given by Gudi (SIAM J Numer Anal 50 (2012), 657–668) for elliptic nonlocal problem of Kirchhoff type. We discuss the well‐posedness of the weak formulation at continuous as well as at discrete levels. We also derive a priori error estimates for semidiscrete and fully discrete formulations in L2 and H1 norms. Results based on the usual finite element method are provided to confirm the theoretical estimates. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 786–813, 2017

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In this paper, we present a finite element scheme with Crank–Nicolson method for solving nonlocal parabolic problems involving the Dirichlet energy. We discuss the well-posedness of the weak formulation at continuous as well as at discrete levels. We derive a priori error estimates for both semi-discrete and fully-discrete formulations. Results based on usual finite element method are provided to confirm the theoretical estimates.

In this paper, we discuss the approximation of p-Laplace problem using WEB-Spline based mesh free finite elements. Along with usual weak formulation, we also consider the mixed formulation of the pLaplace problem. We give existence, uniqueness results for both continuous and discrete problems. We also provide a priori error estimates for both the formulations.

Callus culture of CHRYSANTHEMUM CINERARIAEFOLIUM (Trev.) Bocc. (Asteraceae), initiated with axillary buds from the plant, have been shown to produce chrysanthemyl alcohol and chrysanthemic acid. Incubation of a cell-free homogenate from the callus with [1- (14)C]-isopentenyl pyrophosphate demonstrated incorporation of radioactivity into chrysanthemyl alcohol and chrysanthemic acid as well as products from isopentenyl pyrophosphate isomerase (EC 5.3.3.2; isopentenyl diphosphate Delta (3)-Delta (2)-isomerase) and prenyltransferase activities (EC 2.5.1.11; allylic-terpene-diphosphate:isopentenyl diphosphate terpenoid-allyltransferase).