@Article{CiCP-23-2,
author = {},
title = {An Enriched Multiscale Mortar Space for High Contrast Flow Problems},
journal = {Communications in Computational Physics},
year = {2018},
volume = {23},
number = {2},
pages = {476--499},
abstract = {<p style="text-align: justify;">Mortar methods are widely used techniques for discretizations of partial
differential equations and preconditioners for the algebraic systems resulting from the
discretizations. For problems with high contrast and multiple scales, the standard mortar
spaces are not robust, and some enrichments are necessary in order to obtain an
efficient and robust mortar space. In this paper, we consider a class of flow problems
in high contrast heterogeneous media, and develop a systematic approach to obtain
an enriched multiscale mortar space. Our approach is based on the constructions of
local multiscale basis functions. The multiscale basis functions are constructed from
local problems by following the framework of the Generalized Multiscale Finite Element
Method (GMsFEM). In particular, we first create a local snapshot space. Then we
select the dominated modes within the snapshot space using an appropriate Proper
Orthogonal Decomposition (POD) technique. These multiscale basis functions show
better accuracy than polynomial basis for multiscale problems. Using the proposed
multiscale mortar space, we will construct a multiscale finite element method to solve
the flow problem on a coarse grid and a preconditioning technique for the fine scale
discretization of the flow problem. In particular, we develop a multiscale mortar mixed
finite element method using the mortar space. In addition, we will design a two-level
additive preconditioner and a two-level hybrid preconditioner based on the proposed
mortar space for the iterative method applied to the fine scale discretization of the
flow problem. We present several numerical examples to demonstrate the efficiency
and robustness of our proposed mortar space with respect to both the coarse multiscale
solver and the preconditioners.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0147},
url = {https://global-sci.com/article/80017/an-enriched-multiscale-mortar-space-for-high-contrast-flow-problems}
}