scholarly journals Adaptive modelling of variably saturated seepage problems

2021 ◽  
Author(s):  
B Ashby ◽  
C Bortolozo ◽  
A Lukyanov ◽  
T Pryer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Water Flux ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Posteriori Error Estimate ◽  
Adaptive Finite Element ◽  
Element Method

Summary In this article, we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy–Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific target quantity. The quantity of interest is chosen as volumetric water flux across the seepage face, and therefore depends on an a priori unknown free boundary. We apply our method to challenging numerical examples as well as specific case studies, from which this research originates, illustrating the major difficulties that arise in practical situations. We summarise extensive numerical results that clearly demonstrate the designed method produces rapid error reduction measured against the number of degrees of freedom.

Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

2011 ◽  
Vol 10 (2) ◽  
pp. 339-370 ◽  
Author(s):  
Yunqing Huang ◽  
Hengfeng Qin ◽  
Desheng Wang ◽  
Qiang Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Adaptive Procedure ◽  
Seamless Integration ◽  
Practical Applications ◽  
Element Method

AbstractWe present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptive procedure is developed. As demonstrated by the numerical examples, the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

3D direct current resistivity modeling with unstructured mesh by adaptive finite-element method

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. H7-H17 ◽  
Author(s):  
Zhengyong Ren ◽  
Jingtian Tang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Direct Current ◽  
Homogeneous Model ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Resistivity Modeling ◽  
Element Method

A new adaptive finite-element method for solving 3D direct-current resistivity modeling problems is presented. The method begins with an initial coarse mesh, which is then adaptively refined wherever a gradient-recovery-based a posteriori error estimator indicates that refinement is necessary. Then the problem is solved again on the new grid. The alternating solution and refinement steps continue until a given error criterion is satisfied. The method is demonstrated on two synthetic resistivity models with known analytical solutions, so the errors can be quantified. The applicability of the numerical method is illustrated on a 2D homogeneous model with a topographic valley. Numerical results show that this method is efficient and accurate for geometrically complex situations.

scholarly journals An Adaptive Finite Element Method for Stationary Incompressible Thermal Flow Based on Projection Error Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Zhili Guo ◽  
Jian Su ◽  
Hao Chen ◽  
Xiaomin Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stationary Flow ◽  
Adaptive Strategy ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Thermal Flow ◽  
Element Method

An adaptive finite element method is presented for the stationary incompressible thermal flow problems. A reliable a posteriori error estimator based on a projection operator is proposed and it can be computed easily and implemented in parallel. Finally, three numerical examples are given to illustrate the efficiency of the adaptive finite element method. We also show that the adaptive strategy is effective to detect local singularities in the physical model of square cavity stationary flow in the third example.

scholarly journals An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Nikolay Koshev ◽  
Larisa Beilina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bounded Operator ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Fredholm Integral Equations ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Element Method

AbstractWe propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally simulated and experimental backscattered data measured in microtomography.

Three Dimensional Dynamic Analyses on Stroller Wheel with Shock Absorber

2013 ◽  
Vol 387 ◽  
pp. 159-163
Author(s):  
Yi Chern Hsieh ◽  
Minh Hai Doan ◽  
Chen Tai Chang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
The Road ◽  
Dimensional Finite Element ◽  
On The Road ◽  
Three Dimensional Finite Element ◽  
Element Method

We present the analyses of dynamics behaviors on a stroller wheel by three dimensional finite element method. The vibration of the wheel system causes by two different type barriers on the road as an experiment design to mimic the real road conditions. In addition to experiment analysis, we use two different packages to numerically simulate the wheel system dynamics activities. Some of the simulation results have good agreement with the experimental data in this research. Other interesting data will be measured and analyzed by us for future study and we will investigate them by using adaptive finite element method for increasing the precision of the computation results.

Sign in / Sign up

Export Citation Format

Share Document