application‎ ‎of the‎ ‎hybridized discontinuous galerkin method for solving one-dimensional coupled burgers equations

‎this paper is devoted to proposing hybridized discontinuous galerkin (hdg) approximations for solving a system of coupled burgers equations (cbe) in a closed interval‎. ‎the noncomplete discretized hdg method is designed for a nonlinear weak form of one-dimensional $x-$variable such that numerical fluxes are defined properly‎, ‎stabilization parameters are applied‎, ‎and broken sobolev approximation spaces are exploited in this scheme‎. ‎having necessary conditions on the stabilization parameters‎, ‎it is proven in a theorem and corollary that the proposed method is stable with imposed homogeneous dirichlet and/or periodic boundary conditions to cbe‎. ‎the desired hdg method is stated by using the crank-nicolson method for time-variable discretization and the newton-raphson method for solving nonlinear systems‎. ‎numerical experiences show that the optimal rate of convergence is gained for approximate solutions and their first derivatives‎.