Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

In this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining technique oversampling, one makes use information current residuals to adaptively construct functions in stage reduce error approximation. A complete analysis method is presented, which shows proposed leads fast convergence from approximation fine-scale solution. The reduction can be made sufficiently large by suitably selecting oversampling regions and number layers. Further, rate algorithm depends on factor exponential decay regarding layers user-defined parameter. Numerical results are provided demonstrate effectiveness efficiency adaptive algorithm.