Department of Mathematics

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Author: search.filters.author.Yadav, SangitaHas files: No

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Now showing 1 - 10 of 22
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    Hybridizable discontinuous galerkin method for strongly damped wave problem
    (Springer, 2025-01) Yadav, Sangita
    We introduce and analyze a hybridizable discontinuous Galerkin (HDG) approach for the strongly damped linear wave equation. In our investigation, we derive a priori error estimates to demonstrate the optimal convergence of the approximations for both the solution and its gradient. Further, with the help of the dual problem, we present a post-processed solution and analyze its convergence rate, which is of order for , where k is the degree of the polynomial. We also propose a fully discrete scheme, which is of . To validate our theoretical findings, we perform numerical experiments.
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    Convergence analysis of virtual element methods for the Sobolev equation with convection
    (Springer, 2025-07) Yadav, Sangita
    We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and -norm. Several numerical experiments are conducted to validate the theoretical findings and assess the computational efficiency of the proposed numerical methods.
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    Hybridizable discontinuous Galerkin method for nonlinear hyperbolic integro-differential equations
    (Elsevier, 2025-08) Yadav, Sangita
    In this paper, we present the hybridizable discontinuous Galerkin (HDG) method for a nonlinear hyperbolic integro-differential equation. We discuss the semi-discrete and fully-discrete error analysis of the method. For the semi-discrete error analysis, an extended type mixed Ritz-Volterra projection is introduced for the model problem. It helps to achieve the optimal order of convergence for the unknown scalar variable and its gradient. Further, a local post-processing is performed, which helps to achieve super-convergence. Subsequently, by employing the central difference scheme in the temporal direction and applying the mid-point rule for discretizing the integral term, a fully discrete scheme is formulated, accompanied by its corresponding error estimates. Ultimately, through the examination of numerical examples within two-dimensional domains, computational findings are acquired, thus validating the results of our study.
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    A priori error estimates for sobolev equation using HDG method
    (Springer, 2025-08) Yadav, Sangita
    A hybridizable discontinuous Galerkin (HDG) method is introduced and analyzed to solve the Sobolev equation. The analysis includes the derivation of a priori error estimates, demonstrating that the approximations for both the flux and displacement exhibit convergence at a rate of order where h represents the mesh size and k is the polynomial degree. Additionally, the solution is further improved by applying a post-processing technique, and it has been demonstrated that, for , the post-processed solution converges at an enhanced rate of order . A fully discrete scheme is also proposed, achieving second-order accuracy in time; numerical results are needed to validate the theoretical results.
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    Entropy generation and heat transfer in nonlinear Buoyancy–driven Darcy–Forchheimer hybrid nanofluids with activation energy
    (De Gruyter, 2025-04) Sharma, Bhupendra Kumar; Yadav, Sangita
    This study investigates the influence of a magnetic field, activation energy, and heat source on the heat and mass transfer within a cross fluid embedded with mono-, di-, and tri-nanoparticles, considering thermal radiation and Darcy–Forchheimer effects. Utilizing the Cattaneo–Christov theory, non-Fourier heat transfer is modeled for a vertical moving surface. A mathematical model is developed and subsequently converted into a dimensionless form through an appropriate similarity transformation, resulting in a system of first-order ordinary differential equations. The numerical approach to solve the system is BVP4C solver in MATLAB, a tool specifically designed for boundary value problems. Graphical representations have been analyzed for velocity profiles, temperature profiles, and concentration distributions for different values of physical parameters. It is observed that the velocity profiles exhibit an upward trend with an increase in the parameters associated with nonlinear thermal convection and nonlinear concentration convection. Additionally, the analysis of surface shear stress, heat transfer coefficients, and mass transfer coefficients revealed that an increase in the porosity parameter and Forchheimer number results in decreased shear stress. Entropy generation is also investigated to quantify irreversibilities in the system. The analysis showed that increasing the Brinkman number, diffusion parameter, and temperature and concentration difference parameters leads to higher entropy generation, indicating greater irreversibility in the system. A comparative analysis demonstrates that tri-nanoparticles substantially improve flow velocity, thermal conductivity, and solute diffusion compared to di- and mono-nanoparticles, with tri-nanofluids exhibiting the most optimal overall performance.
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    Optimal L2 estimates for the semidiscrete galerkin method applied to parabolic integro-differential equations with nonsmooth data
    (CUP, 2024-06) Yadav, Sangita
    We propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain
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    Legendre wavelet modified petrov–galerkin method in two-dimensional moving boundary problem
    (De Gruyter, 2017-12) Yadav, Sangita
    In this study, we developed the two-dimensional Legendre wavelet modified Petrov–Galerkin method for solving the two-dimensional moving boundary problem arising during melting of solid whose one surface is kept under most generalised boundary condition, and other two surfaces are insulated. The particular cases when surface subjected to the boundary condition of first, second and third kinds are discussed in detail. For validity of the present method, we have plotted graphs between residual (obtained from the original differential equation and its associated boundary conditions) and x-axis and found the effect of an error on moving layer thickness and y coordinate, respectively. Furthermore, we proved the convergence analysis of present method. The effect of parameters (Predvoditelev number, Kirpichev number, Biot number) on the moving layer thickness is discussed in detail. The whole analysis is presented in a dimensionless form.
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    Backward euler method for 2d sobolev equation with burgers’ type non-linearity
    (AIP, 2023-06) Yadav, Sangita
    Backward Euler for two dimensional Sobolev equation is discussed in this article. We begin by obtaining some basic a priori estimates for the semi-discrete scheme and for the backward Euler approximation. It is proven that these estimations for the discrete scheme are valid uniformly in time using the discrete Gronwall’s Lemma. In addition, the presence of a discrete global attractor is established. Furthermore, optimal a priori error bounds are determined, which are time dependent exponentially. Under the uniqueness condition, these error estimates are demonstrated to be uniform in time. Finally, we establish several numerical examples that validate our theoretical approach.
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    Hdg method for linear parabolic integro-differential equations
    (Elsevier, 2023-08) Yadav, Sangita
    This paper develops the hybridizable discontinuous Galerkin (HDG) method for a linear parabolic integro-differential equation and analyzes uniform in time error bounds. To handle the integral term, an extended Ritz-Volterra projection is introduced, which helps in achieving optimal order convergence of for the semi-discrete problem when polynomials of degree are used to approximate both the solution and the flux variables. Further, element-by-element post-processing is proposed, and it is established that it achieves convergence of the order for . Using the backward Euler method in temporal direction and quadrature rule to discretize the integral term, a fully discrete scheme is derived along with its error estimates. Finally, with the help of numerical examples in two-dimensional domains, computational results are obtained, which verify our results.
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    Mixed virtual element method for integro-differential equations of parabolic type
    (Springer, 2024-04) Yadav, Sangita
    This article presents and analyzes a mixed virtual element approach for discretizing parabolic integro-differential equations in a bounded subset of , in addition to the backward Euler approach for temporal discretization. With the help of the intermediate projection along with Fortin and projections, we effectively tackle the treatment of integral terms in both the fully discrete and semi-discrete analysis. This inclusion leads to the derivation of optimal a priori error estimates with an order of for the two unknowns. Furthermore, we present a systematic analysis that outlines the step-by-step process for achieving super convergence of the discrete solution, with an order of . Several computational experiments are discussed to validate the proposed scheme’s computational efficiency and support the theoretical conclusions.