TY - JOUR T1 - Superconvergence and a Posteriori Error Estimates of a Local Discontinuous Galerkin Method AU - MAHBOUB BACCOUCH JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 188 EP - 216 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/230.html KW - Local discontinuous Galerkin method KW - fourth-order initial-boundary value problems KW - Euler-Bernoulli beam equation KW - superconvergence KW - a posteriori error estimates AB - In this paper, we investigate the superconvergence properties and a posteriori error estimates of a local discontinuous Galerkin (LDG) method for solving the one-dimensional linear fourth-order initial-boundary value problems arising in study of transverse vibrations of beams. We present a local error analysis to show that the leading terms of the local spatial discretization errors for the k-degree LDG solution and its spatial derivatives are proportional to (k+1)-degree Radau polynomials. Thus, the k-degree LDG solution and its derivatives are O(h^{k+2}) superconvergent at the roots of (k+1)-degree Radau polynomials. Computational results indicate that global superconvergence holds for LDG solutions. We discuss how to apply our superconvergence results to construct efficient and asymptotically exact a posteriori error estimates in regions where solutions are smooth. Finally, we present several numerical examples to validate the superconvergence results and the asymptotic exactness of our a posteriori error estimates under mesh refinement. Our results are valid for arbitrary regular meshes and for P^k polynomials with k ≥ 1, and for various types of boundary conditions.

MAHBOUB BACCOUCH. (2014). Superconvergence and a Posteriori Error Estimates of a Local Discontinuous Galerkin Method. International Journal of Numerical Analysis Modeling Series B. 5 (3). 188-216. doi: