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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)
  • Received : 2019.07.08
  • Accepted : 2019.09.14
  • Published : 2019.09.25

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.

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