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http://dx.doi.org/10.12941/jksiam.2020.24.039

OPTIMAL ERROR ESTIMATE OF A DECOUPLED CONSERVATIVE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE KLEIN-GORDON-SCHRÖDINGER EQUATIONS  

YANG, HE (DEPARTMENT OF MATHEMATICS, AUGUSTA UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.24, no.1, 2020 , pp. 39-78 More about this Journal
Abstract
In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.
Keywords
conservative local discontinuous Galerkin methods; error estimates; Klein-Gordon-$Schr{\ddot{o}}dinger$ equations;
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