Superconvergence of the Direct Discontinuous Galerkin Method for Two-Dimensional Nonlinear Convection-Diffusion Equations

11/07/2021
by   Xinyue Zhang, et al.
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This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for two-dimensional nonlinear convection-diffusion equations. By using the idea of correction function, we prove that, for any piecewise tensor-product polynomials of degree k≥ 2, the DDG solution is superconvergent at nodes and Lobatto points, with an order of O(h^2k) and O(h^k+2), respectively. Moreover, superconvergence properties for the derivative approximation are also studied and the superconvergence points are identified at Gauss points, with an order of O(h^k+1). Numerical experiments are presented to confirm the sharpness of all the theoretical findings.

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