Papers by Ayan Chakraborty
Differential Equations and Dynamical Systems, Nov 20, 2020
We propose a non uniform web spline based finite element analysis for elliptic partial differenti... more We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of O(h α ) for α > 0.
Differential Equations and Dynamical Systems, 2020
We propose a non uniform web spline based finite element analysis for elliptic partial differenti... more We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of O(h α ) for α > 0.
International Journal of Advances in Engineering Sciences and Applied Mathematics, 2018
In this study we establish the existence and uniqueness of the solution of a coupled system of ge... more In this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion , non-uniform advection and variably influencing reaction terms on Lipschitz continuous domain Ω ⊂ R m (m≥1) with a Dirichlet boundary. Later we consider the finite element (FE) approximation of the coupled equations in a meshless framework based on weighted extended B-Spine functions (WEBS).The a priori error estimates corresponding to the finite element analysis are derived to establish the convergence of the corresponding FE scheme and the numerical methodology has been tested on few examples.

Finite element method for drifted space fractional tempered diffusion equation
Journal of Applied Mathematics and Computing, 2019
Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are f... more Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in different field of science have been reconsidered in this terms like diffusion wave equations, Schr$$\ddot{o}$$o¨dinger equation and so on. In the present paper, a time dependent tempered fractional diffusion equation of order $$\gamma \in (0,1)$$γ∈(0,1) with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank–Nicolson discretization is used in the time direction. By implementing finite element approximation a priori space–time estimate has been derived and we proved that the convergent order is $$\mathcal {O}(h^2+\varDelta t ^2)$$O(h2+Δt2) where h is the space step size and $$\varDelta t$$Δt is the time difference. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.
arXiv (Cornell University), Jun 24, 2018
arXiv: Numerical Analysis, 2018
We analyze the error of the WEB-S finite element method applied to elliptic systems with non-coop... more We analyze the error of the WEB-S finite element method applied to elliptic systems with non-cooperative dominant coupling,with a mixed Dirichlet/Neumann/Robin boundary condition. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. These results are based on an extensive regularity analysis of the interface problems of concern.Finally, the error analysis is illustrated by numerical experiments.
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Papers by Ayan Chakraborty