33 citations · 49 across the 25 of their papers we have counts for
31 papers
Quasi-optimality of adaptive FEM for optimal control problems involving Dirac measures governed by biharmonic equation
Asha K. Dond, Neela Nataraj, Subham Nayak
This article establishes the quasi-optimality of adaptive nonconforming finite element methods for a class of optimal control problems involving Dirac measures governed by the biha…
Unconditionally stable and energy conserving discretization of the dynamic von Kármán equations
Carsten Carstensen, Neela Nataraj, Ricardo Ruiz-Baier +1
A fully discrete approximation of the dynamic von Kármán equations combines nonconforming Morley finite element methods for spatial discretization with an energy conserving modifie…
Hybrid-high order method in space and implicit schemes in time for the biharmonic wave equation
Raman Kumar, Neela Nataraj, Aamir Yousuf
This article presents the numerical analysis for the biharmonic wave equation with clamped boundary conditions employing two variants of the {hybrid high-order} method for the spac…
Unified numerical analysis for thermoelastic diffusion and thermo-poroelasticity of thin plates
Neela Nataraj, Ricardo Ruiz-Baier, Aamir Yousuf
We investigate a coupled hyperbolic-parabolic system modeling thermoelastic diffusion (resp. thermo-poroelasticity) in plates, consisting of a fourth-order hyperbolic partial diffe…
Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem
Neela Nataraj, Ricardo Ruiz-Baier, Aamir Yousuf
This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equat…
Lowest-order Nonstandard Finite Element Methods for Time-Fractional Biharmonic Problem
Shantiram Mahata, Neela Nataraj, Jean-Pierre Raymond
In this work, we consider an initial-boundary value problem for a time-fractional biharmonic equation in a bounded polygonal domain with a Lipschitz continuous boundary in $\mathbb…
Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation
Carsten Carstensen, Benedikt Gräßle, Neela Nataraj
An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-or…
A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity
Carsten Carstensen, Benedikt Gräßle, Neela Nataraj
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general sourc…
Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems
Carsten Carstensen, Neela Nataraj, Gopikrishnan C. Remesan +1
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods…
Feedback stabilization of parabolic coupled system and its numerical study
Wasim Akram, Debanjana Mitra, Neela Nataraj +1
In the first part of this article, we study feedback stabilization of a parabolic coupled system by using localized interior controls. The system is feedback stabilizable with expo…
Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem
Rekha Khot, Neela Nataraj, Nitesh Verma
This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inver…
Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs
C. Carstensen, Neela Nataraj, Amiya K. Pani
For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients in and symmetric and uniformly positive d…
A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations
Sudipto Chowdhury, Asha K. Dond, Neela Nataraj +1
This article discusses numerical analysis of the distributed optimal control problem governed by the von Kármán equations defined on a polygonal domain in . The state…
Parameter dependent finite element analysis for ferronematics solutions
Ruma Rani Maity, Apala Majumdar, Neela Nataraj
This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of…
A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified righthand sides
Carsten Carstensen, Neela Nataraj
This article on nonconforming schemes for harmonic problems simultaneously treats the Crouzeix-Raviart () and the Morley finite elements () for the original and for m…
Lowest-order equivalent nonstandard finite element methods for biharmonic plates
Carsten Carstensen, Neela Nataraj
The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the interior…
Morley Finite Element Method for the von Kármán Obstacle Problem
Carsten Carstensen, Sharat Gaddam, Neela Nataraj +2
This paper focusses on the von Kármán equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilin…
Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem
Ruma Rani Maity, Apala Majumdar, Neela Nataraj
We study a system of semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-…
Hessian discretisation method for fourth order semi-linear elliptic equations: applications to the von Kármán and Navier--Stokes models
Jérome Droniou, Neela Nataraj, Devika Shylaja
This paper deals with the Hessian discretisation method (HDM) for fourth order semi-linear elliptic equations with a trilinear nonlinearity. The HDM provides a generic framework fo…
Convergence analysis of a numerical scheme for a tumour growth model
Jerome Droniou, Neela Nataraj, Gopikrishnan Chirappurathu Remesan
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumo…
Adaptive Morley FEM for the von Kármán equations with optimal convergence rates
Carsten Carstensen, Neela Nataraj
The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von Kármán equations with optimal convergence rates for sufficiently fine trian…
Discontinuous Galerkin Finite Element Methods for the Landau-de Gennes Minimization Problem of Liquid Crystals
Ruma Rani Maity, Apala Majumdar, Neela Nataraj
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liqu…
Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations
Gouranga Mallik, Neela Nataraj, Jean-Pierre Raymond
In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise co…
A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite Element Methods for the Von Kármán Equations
Carsten Carstensen, Gouranga Mallik, Neela Nataraj
This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von Kármán equations defined on a polygonal domain. A discrete in…