Department of Mathematics
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Item Hybridizable discontinuous galerkin method for strongly damped wave problem(Springer, 2025-01) Yadav, SangitaWe 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.Item A priori error estimates for sobolev equation using HDG method(Springer, 2025-08) Yadav, SangitaA 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.Item Legendre wavelet modified petrov–galerkin method in two-dimensional moving boundary problem(De Gruyter, 2017-12) Yadav, SangitaIn 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.