The solution of a high-order conduction problem with different orders of accuracy has been investigated in this paper. The high-order solutions are obtained using Discontinuous Galerkin (DG) finite element method. The problem is solved by implicit Newton-Krylov method for different accuracy orders. The convergence of the implicit technique is investigated in terms of the CPU time. The results show the possibility of achieving an accurate and smooth solution over a coarse mesh when the higher-order discretization is employed.

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