An Adaptive Discontinuous Galerkin Multiscale Method for Elliptic Problems

An adaptive discontinuous Galerkin multiscale method driven by an energy norm a posteriori error bound is proposed. The method is based on splitting the problem into a coarse and fine scale. Localized fine scale constituent problems are solved on patches of the domain and are used to obtain a modified coarse scale equation. The coarse scale equation has considerably less degrees of freedom than the original problem. The a posteriori error bound is used within an adaptive algorithm to tune the critical parameters, i.e., the refinement level and the size of the different patches on which the fine scale constituent problems are solved. The fine scale computations are completely parallelizable, since no communication between different processors is required for solving the constituent fine scale problems. The convergence of the method, the performance of the adaptive strategy, and the computational effort involved are investigated through a series of numerical experiments.