scholarly journals An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

2010 ◽  
Vol 229 (21) ◽  
pp. 8072-8094 ◽  
Author(s):  
Xianping Li ◽  
Weizhang Huang
Keyword(s):  
Finite Element ◽  
Anisotropic Diffusion ◽  
Mesh Adaptation ◽  
Finite Element Solution ◽  
Element Solution ◽  
Anisotropic Mesh ◽  
Anisotropic Mesh Adaptation ◽  
Adaptation Method ◽  
Diffusion Problems

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

2017 ◽  
Vol 10 (4) ◽  
pp. 913-940 ◽  
Author(s):  
Xianping Li ◽  
Weizhang Huang
Keyword(s):  
Maximum Principle ◽  
Reservoir Simulation ◽  
Anisotropic Diffusion ◽  
Mesh Adaptation ◽  
Element Solution ◽  
Fractured Reservoir ◽  
Anisotropic Mesh ◽  
The Maximum Principle ◽  
Anisotropic Mesh Adaptation ◽  
Diffusion Problems

AbstractAnisotropic 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.

scholarly journals High order optimal anisotropic mesh adaptation using hierarchical elements

2012 ◽  
Author(s):  
R. Bois ◽  
M Fortin ◽  
A. Fortin ◽  
A Couët
Keyword(s):  
Finite Element ◽  
Mesh Adaptation ◽  
Finite Element Solution ◽  
Element Solution ◽  
Anisotropic Mesh ◽  
Anisotropic Meshes ◽  
The Past ◽  
Discretisation Error ◽  
Anisotropic Mesh Adaptation ◽  
Lagrange Finite Element

Anisotropic mesh adaptation has made spectacular progress in the past few years. The introduction of the notion of a metric, directly linked to the interpolation error, has allowed to control the elongation of elements as well as the discretisation error. This approach is however essentially restricted to linear (P(1)) finite element solutions, though there exists some generalisations. A completely general approach leading to optimal meshes and this, for finite element solution of any degree, is still missing. This is precisely the goal of this work where we show how to estimate the error on a finite element solution of degree k using hierarchical basis for Lagrange finite element polynomials. We then show how to use this information to produce optimal anisotropic meshes in a sense that will be precised.

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