Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient.
File(s)upscaledHDG_Brinkman_version3.pdf (426.41 KB)
Accepted version
Author(s)
Li, G
Shi, Ke
Type
Journal Article
Abstract
In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that depend on the high-contrast coefficient weakly. Due to the heterogeneity of the problem, a huge global system will be produced after the numerical discretization of HDG method. Thanks to the upscaled structure of the proposed methods, we are able to reduce the huge global system onto the skeleton of the coarse mesh only while still capturing important fine scale features of this problem. The finite element space over the coarse mesh is irrelevant to the fine scale computation. This feature makes our proposed method very attractive. Several numerical examples are presented to support our theoretical findings.
Date Issued
2018-12-01
Date Acceptance
2018-04-30
Citation
Journal of Scientific Computing, 2018, 77 (3), pp.1780-1800
ISSN
0885-7474
Publisher
Springer Verlag
Start Page
1780
End Page
1800
Journal / Book Title
Journal of Scientific Computing
Volume
77
Issue
3
Copyright Statement
© 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018. The final publication is available at Springer via https://doi.org/10.1007/s10915-018-0725-7
Identifier
https://link.springer.com/article/10.1007%2Fs10915-018-0725-7
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Multiscale FEM
Brinkman equation
Hybridizable
DG methods
FINITE-ELEMENT-METHOD
POROUS-MEDIA
STOKES-FLOW
SUPERCONVERGENCE
CONSTRUCTION
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2018-05-16