TY - JOUR
T1 - An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media
AU - Eric T. Chung, Yalchin Efendiev & Wing Tat Leung
JO - Communications in Computational Physics
VL - 2
SP - 401
EP - 422
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.230815.090516a
UR - https://global-sci.org/intro/article_detail/cicp/11243.html
KW - 
AB - <p style="text-align: justify;">Offline computation is an essential component in most multiscale model
reduction techniques. However, there are multiscale problems in which offline procedure
is insufficient to give accurate representations of solutions, due to the fact that
offline computations are typically performed locally and global information is missing
in these offline information. To tackle this difficulty, we develop an online local
adaptivity technique for local multiscale model reduction problems. We design new
online basis functions within Discontinuous Galerkin method based on local residuals
and some optimally estimates. The resulting basis functions are able to capture
the solution efficiently and accurately, and are added to the approximation iteratively.
Moreover, we show that the iterative procedure is convergent with a rate independent
of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline
on how to choose the initial space. We present some numerical examples to show
the performance of the proposed method.</p>