Multilevel correction goal-oriented adaptive finite element method for semilinear elliptic equations

Author(s):  
Fei Xu ◽  
Qiumei Huang ◽  
Huiting Yang ◽  
Hongkun Ma
2013 ◽  
Vol 387 ◽  
pp. 159-163
Author(s):  
Yi Chern Hsieh ◽  
Minh Hai Doan ◽  
Chen Tai Chang

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.


Author(s):  
B Ashby ◽  
C Bortolozo ◽  
A Lukyanov ◽  
T Pryer

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.


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