TY - JOUR
T1 - The Multiscale Discontinuous Galerkin Method for Solving a Class of Second Order Elliptic Problems with Rough Coefficients
AU - Wang , W.
AU - Guzmán , J.
AU - Shu , C.-W.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 28
EP - 47
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/672.html
KW - multiscale discontinuous Galerkin method, rough coefficients.
AB - <p style="text-align: justify;">We develop a multiscale discontinuous Galerkin (DG) method for solving a class
of second order elliptic problems with rough coefficients. The main ingredient of this method
is to use a non-polynomial multiscale approximation space in the DG method to capture the
multiscale solutions using coarse meshes without resolving the fine scale structure of the solution.
Theoretical proofs and numerical examples are presented in both one and two dimensions. For
one-dimensional problems, optimal error estimates and numerical examples are shown for arbitrary
order approximations. For two-dimensional problems, numerical results are presented by the high
order multiscale DG method, but the error estimate is proven only for the second order method.</p>