Skip to main content
    • Aa
    • Aa

Anisotropic Mesh Adaptation for 3D Anisotropic Diffusion Problems with Application to Fractured Reservoir Simulation

  • Xianping Li (a1) and Weizhang Huang (a2)

Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The 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 improving the satisfaction of the maximum principle.

Corresponding author
*Corresponding author. Email addresses: (X. P. Li), (W. Z. Huang)
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 2
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 50 *
Loading metrics...

* Views captured on Cambridge Core between 12th September 2017 - 19th October 2017. This data will be updated every 24 hours.