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An Optimal A Posteriori Error Estimates Of The Local Discontinuous Galerkin Method For The Second-Order Wave Equation In One Space Dimension, Mahboub Baccouch
An Optimal A Posteriori Error Estimates Of The Local Discontinuous Galerkin Method For The Second-Order Wave Equation In One Space Dimension, Mahboub Baccouch
Mathematics Faculty Publications
In this paper, we provide the optimal convergence rate of a posteriori error estimates for the local discontinuous Galerkin (LDG) method for the second-order wave equation in one space dimension. One of the key ingredients in our analysis is the recent optimal superconvergence result in [W. Cao, D. Li and Z. Zhang, Commun. Comput. Phys. 21 (1) (2017) 211-236]. We first prove that the LDG solution and its spatial derivative, respectively, converge in the L 2 -norm to (p + 1)-degree right and left Radau interpolating polynomials under mesh refinement. The order of convergence is proved to be p + …