Multiscale HDG model reduction method for flows in heterogeneous porous media

摘要

In this research, we give projection-based error analysis on a multiscale hybridizable discontinuous Galerkin method to numerically solve parabolic problem with a heterogeneous coefficient. We modified the spectral multiscale HDG method introduced in [22] to fit to the time-dependent PDE. The method uses multiscale spaces generated by eigenfunctions of local spectral problems. By considering two different grids, one relatively coarser than the other, we give bounds for the error between the actual solution and the approximate one derived from multiscale HDG method. One of the main focuses of the paper is to derive error analysis that depends on the size of fine and coarse grids and eigenvalues of local spectral problems. To solve a given coarse problem, the more eigenfunction we choose, the more accurate the approximation becomes: we shall see that the numerical result indicates that when we fix fine and coarse grids, the error between the reference solution and the derived one decreases whenever we have more multiscale basis functions. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.