Anisotropic mesh adaptation for 3D anisotropic diffusion problems with application to fractured reservoir simulation
Department of Mathematics and Statistics, the University of Missouri-Kansas City（密苏里大学堪萨斯城分校数学与统计系）；Department of Mathematics, the University of Kansas（堪萨斯大学数学系）
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.
Generalized Multiscale Multicontinuum Model for Fractured Vuggy Carbonate Reservoirs
Texas A&M University（德州农工大学）；The Chinese University of Hong Kong（香港中文大学）；North-Eastern Federal University（东北联邦大学）；Texas A&M University at Qatar（卡塔尔德州农工大学）
A novel equi-dimensional finite element method for flow and transport in fractured porous media satisfying discrete maximum principle and conservation properties
A Localized Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems
Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院应用与数值数学研究所）；Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学数学科学系）
A posteriori error estimation for coarse or distorted meshes
Universidad de la República（乌拉圭共和国大学）；Université de Strasbourg（斯特拉斯堡大学）；Inria（法国国家数字研究院）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Univ. Lille（里尔大学）；Arts et Métiers Institute of Technology（巴黎高科艺术工艺学院）；Centrale Lille（里尔中央理工学院）；Junia（朱尼亚应用科学联盟）
A hybrid finite volume -- finite element method for bulk--surface coupled problems
Institute of Numerical Mathematics, Russian Academy of Sciences（俄罗斯科学院数值数学研究所）；Department of Mathematics, University of Houston（休斯顿大学数学系）；Sechenov University（谢切诺夫大学）
Rheinische Friedrich-Wilhelms-Universität Bonn（波恩大学）；Institute for Numerical Simulation（数值模拟研究所）；Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学数学科学系）
