Yazar "Natesan, Srinivasan" seçeneğine göre listele

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    Öğe
    A parameter-uniform hybrid method for singularly perturbed parabolic 2D convection-diffusion-reaction problems
    (Elsevier, 2025) Barman, Mrityunjoy; Natesan, Srinivasan; Sendur, Ali
    The solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy.
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    Error estimates for a fully discrete epsilon-uniform finite element method on quasi uniform meshes
    (2021) Şendur, Ali; Natesan, Srinivasan; Singh, Gautam
    In this article, we analyze a fully discrete epsilon-uniformly convergent finite element method for singularly perturbed convection-diffusion-reaction boundary-value problems, on piecewise-uniform meshes. Here, we choose L-splines as basis functions. We will concentrate on the convergence analysis of the finite element method which employ the discrete L-spline basis functions instead of their continuous counterparts. The L-splines are approximated on the piecewise-uniform Shishkin mesh inside each element. These approximations are used as basis functions in the frame of Galerkin FEM on a coarse piecewise-uniform mesh to discretize the domain. Further, we determine the amount of error introduced by the discrete L-spline basis functions in the overall numerical method, and explore the possibility of recovering the order of convergence that are consistent with the classical order of convergence for the numerical methods using the exact L-splines.
  • Küçük Resim
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    Error estimates for a fully discrete varepsilon?uniform finite element methodon quasi uniform meshes
    (2021) Şendur, Ali; Natesan, Srinivasan; Singh, Gautam
    In this article, we analyze a fully discrete varepsilon?uniformly convergent finite element method for singularly perturbed convection-diffusion-reaction boundary-value problems, on piecewise-uniform meshes. Here, we choose L?splines as basis functions.We will concentrate on the convergence analysis of thefinite element methodwhich employ the discreteL?spline basis functions instead of their continuous counterparts.The L?splines are approximated on the piecewise-uniform Shishkin mesh inside each element. These approximations are used as basis functions in the frame of Galerkin FEM on a coarse piecewise-uniform meshto discretize the domain. Further, we determinethe amount of error introduced by the discrete L?spline basis functions in the overall numerical method, and explore the possibility of recovering the order of convergence that are consistent with the classical order of convergence for the numerical methods usingthe exact L?splines.
  • [ X ]
    Öğe
    Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection - diffusion - reaction problems
    (Taylor & Francis Ltd, 2023) Singh, Gautam; Natesan, Srinivasan; Sendur, Ali
    This article focuses on constructing and analyzing a non-symmetric interior penalty Galerkin method (NIPG) on Shishkin mesh for solving singularly perturbed 2D elliptic boundary-value problems (BVPs). We use piecewise Lagrange interpolation at Gaussian points to improve the order of convergence of the interpolation error. We then study the superconvergence properties of the NIPG method and prove O(N-1 ln N)(k+1) order of convergence in the discrete energy-norm. Various numerical experiments are provided to validate the theoretical results.