@Article{NMTMA-10-913,
author = {Xianping Li and Weizhang Huang},
title = {Anisotropic Mesh Adaptation for 3D Anisotropic Diffusion Problems with Application to Fractured Reservoir Simulation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2017},
volume = {10},
number = {4},
pages = {913--940},
abstract = {<p style="text-align: justify;">Anisotropic mesh adaptation is studied for linear finite element solution of
3D anisotropic diffusion problems. The&nbsp;$\mathbb{M}$-uniform mesh approach is used, where an
anisotropic adaptive mesh is generated as a uniform one in the metric specified by a
tensor. In addition to mesh adaptation, preservation of the maximum principle is also
studied. Some new sufficient conditions for maximum principle preservation are developed, and a mesh quality measure is defined to server as a good indicator. Four
different metric tensors are investigated: one is the identity matrix, one focuses on minimizing an error bound, another one on preservation of the maximum principle, while
the fourth combines both. Numerical examples show that these metric tensors serve
their purposes. Particularly, the fourth leads to meshes that improve the satisfaction
of the maximum principle by the finite element solution while concentrating elements
in regions where the error is large. Application of the anisotropic mesh adaptation to
fractured reservoir simulation in petroleum engineering is also investigated, where unphysical solutions can occur and mesh adaptation can help to improve the satisfaction
of the maximum principle.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.m1625},
url = {http://global-sci.org/intro/article_detail/nmtma/10462.html}
}