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http://dx.doi.org/10.12941/jksiam.2019.23.211

NUMERICAL COUPLING OF TWO SCALAR CONSERVATION LAWS BY A RKDG METHOD  

OKHOVATI, NASRIN (DEPARTMENT OF MATHEMATICS, KERMAN BRANCH, ISLAMIC AZAD UIVERSITY)
IZADI, MOHAMMAD (DEPARTMENT OF APPLIED MATHEMATICS, FACULTY OF MATHEMATICS AND COMPUTER, SHAHID BAHONAR UNIVERSITY OF KERMAN)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.23, no.3, 2019 , pp. 211-236 More about this Journal
Abstract
This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.
Keywords
Conservation laws; Discontinuous flux; Discontinuous Galerkin methods; Coupling equations; Error estimates;
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