In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms and boundary conditions. The ensemble HDG discrete system shares a common coefficient matrix with multiple right hand side (RHS) vectors; it reduces both computational cost and storage. We have two contributions in this paper. First, we derive an optimal L2 convergence rate for the ensemble solutions on a general polygonal domain, which is the first such result in the literature. Second, we obtain a superconvergent rate for the ensemble solutions after an element-by-element postprocessing under some assumptions on the domain and the coefficients of the PDEs. We present numerical experiments to confirm our theoretical results.
@article{arxiv.1903.04017,
title = {A Superconvergent Ensemble HDG Method for Parameterized Convection Diffusion Equations},
author = {Gang Chen and Liangya Pi and Liwei Xu and Yangwen Zhang},
journal= {arXiv preprint arXiv:1903.04017},
year = {2019}
}