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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17638
Title: On two conservative hdg schemes for nonlinear klein-gordon equation
Authors: Yadav, Sangita
Keywords: Mathematics
Numerical analysis
Hybridizable discontinuous galerkin (HDG)
Issue Date: Nov-2024
Abstract: In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that approximations of the flux and the displacement converge with order O(hk+1), where h is the discretizing parameter and k is the degree of the piecewise polynomials to approximate both flux and displacement variables. After post-processing of the semi-discrete solution, it is shown that the post-processed solution converges with order O(hk+2) for k≥1. Moreover, a second-order conservative finite difference scheme is applied to discretize in time %second-order convergence in time. and it is proved that the discrete energy is conserved with optimal error estimates for the completely discrete method. %Since at each time step, one has to solve a nonlinear system of algebraic equations, To avoid solving a nonlinear system of algebraic equations at each time step, a non-conservative scheme is proposed, and its error analysis is also briefly established. Moreover, another variant of the HDG scheme is analyzed, and error estimates are established. Finally, some numerical experiments are conducted to confirm our theoretical findings.
URI: https://arxiv.org/abs/2411.15572
http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17638
Appears in Collections:Department of Mathematics

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