A Posteriori Error Estimates and an Adaptive Finite Element Method for the Allen–Cahn Equation and the Mean Curvature Flow

@article{Feng2005APE,
  title={A Posteriori Error Estimates and an Adaptive Finite Element Method for the Allen–Cahn Equation and the Mean Curvature Flow},
  author={Xiaobing Feng and Haijun Wu},
  journal={Journal of Scientific Computing},
  year={2005},
  volume={24},
  pages={121-146}
}
This paper develops an a posteriori error estimate of residual type for finite element approximations of the Allen–Cahn equation ut − Δu+ ε−2f(u)=0. It is shown that the error depends on ε−1 only in some low polynomial order, instead of exponential order. Based on the proposed a posteriori error estimator, we construct an adaptive algorithm for computing the Allen–Cahn equation and its sharp interface limit, the mean curvature flow. Numerical experiments are also presented to show the… CONTINUE READING

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Numerical Studies of Discrete Approximations to the Allen--Cahn Equation in the Sharp Interface Limit

  • SIAM J. Scientific Computing
  • 2009
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