TY - JOUR
T1 - An Enriched Petrov-Galerkin Method for Darcy Flow in Fractured Porous Media
AU - Chen , Huangxin
AU - Wang , Zixuan
JO - Annals of Applied Mathematics
VL - 4
SP - 347
EP - 393
PY - 2025
DA - 2025/01
SN - 40
DO - http://doi.org/10.4208/aam.OA-2024-0015
UR - https://global-sci.org/intro/article_detail/aam/23776.html
KW - Discrete fracture model, enriched Petrov-Galerkin method, local mass conservation, post-processing, error analysis.
AB - <p style="text-align: justify;">We develop a locally mass-conservative enriched Petrov-Galerkin
(EPG) method without any penalty term for the simulation of Darcy flow in
fractured porous media. The discrete fracture model is applied to model the fractures as the lower dimensional fracture interfaces. The new method enriches the
approximation trial space of the conforming continuous Galerkin (CG) method
with bubble functions and enriches the approximation test space of the CG
method with piecewise constant functions in the fractures and the surrounding
porous media. We propose a framework for constructing the bubble functions
and consider a decoupled algorithm for the EPG method. The solution of the
pressure can be decoupled into two steps with a standard CG method and a
post-processing correction. The post-processing correction based on the bubble
functions in the matrix and the fractures can be solved separately, which is useful for parallel computing. We derive a priori and a posteriori error estimates for
the problem. Numerical examples are presented to illustrate the performance of
the proposed method.</p>