TY - JOUR AU - Llorente, V´ıctor AU - Rubio, Gonzalo AU - Pascau, Antonio AU - Ferrer, Esteban AU - Arıcı, M¨usl¨um PY - 2017 TI - Comparison of the ENATE approach and discontinuous Galerkin spectral element method in 1D nonlinear transport equations JF - Computer Assisted Methods in Engineering and Science; Vol 23 No 2–3 (2016) KW - N2 - In this paper a comparison of the performance of two ways of discretizing the nonlinear convection-diffusion equation in a one-dimensional (1D) domain is performed. The two approaches can be considered within the class of high-order methods. The first one is the discontinuous Galerkin method, which has been profusely used to solve general transport equations, either coupled as the Navier-Stokes equations, or on their own. On the other hand, the ENATE procedure (Enhanced Numerical Approximation of a Transport Equation), uses the exact solution to obtain an exact algebraic equation with integral coefficients that link nodal values with a three-point stencil. This paper is the first of thorough assessments of ENATE by comparing it with well-established high-order methods. Several test cases of the steady Burgers' equation with and without source have been chosen for comparison. UR - https://cames.ippt.pan.pl/index.php/cames/article/view/168