Verified eigenvalue evaluation for the Laplacian over polygonal domains of arbitrary shape X Liu, S Oishi SIAM Journal on Numerical Analysis 51 (3), 1634-1654, 2013 | 73 | 2013 |

A framework of verified eigenvalue bounds for self-adjoint differential operators X Liu Applied Mathematics and Computation 267, 341-355, 2015 | 53 | 2015 |

Estimation of interpolation error constants for the P0 and P1 triangular finite elements F Kikuchi, X Liu Computer methods in applied mechanics and engineering 196 (37), 3750-3758, 2007 | 50 | 2007 |

Determination of the Babuska-Aziz constant for the linear triangular finite element F Kikuchi, L Xuefeng Japan Journal of Industrial and Applied Mathematics 23 (1), 75, 2006 | 41 | 2006 |

Analysis and estimation of error constants for P0 and P1 interpolations over triangular finite elements X Liu, F Kikuchi J. Math. Sci. Univ. Tokyo 17 (1), 27-78, 2010 | 37 | 2010 |

Verified computations to semilinear elliptic boundary value problems on arbitrary polygonal domains A Takayasu, X Liu, S Oishi Nonlinear Theory and Its Applications, IEICE 4 (1), 34-61, 2013 | 28 | 2013 |

Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation K Tanaka, A Takayasu, X Liu, S Oishi | 17 | 2012 |

Guaranteed high-precision estimation for *P* _{0} interpolation constants on triangular finite elementsX Liu, S Oishi Japan Journal of Industrial and Applied Mathematics 30 (3), 635-652, 2013 | 14 | 2013 |

Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements M Xie, H Xie, X Liu Japan Journal of Industrial and Applied Mathematics 35 (1), 335-354, 2018 | 9 | 2018 |

Explicit finite element error estimates for nonhomogeneous Neumann problems Q Li, X Liu Applications of Mathematics 63 (3), 367-379, 2018 | 7 | 2018 |

Remarks on computable a priori error estimates for finite element solutions of elliptic problems A Takayasu, X Liu, S Oishi Nonlinear Theory and Its Applications, IEICE 5 (1), 53-63, 2014 | 7 | 2014 |

High-precision eigenvalue bound for the Laplacian with singularities X Liu, T Okayama, S Oishi Computer Mathematics, 311-323, 2014 | 6 | 2014 |

A subdivision scheme for volumetric models G Mustafa, L Xuefeng Applied Mathematics-A Journal of Chinese Universities 20 (2), 213-224, 2005 | 6 | 2005 |

Guaranteed eigenvalue bounds for the Steklov eigenvalue problem C You, H Xie, X Liu SIAM Journal on Numerical Analysis 57 (3), 1395-1410, 2019 | 5 | 2019 |

环面构造管道拼接曲面的方法及其连续性 刘雪峰 中国科学技术大学学报 34 (1), 20-28, 2004 | 5 | 2004 |

Explicit bound for quadratic Lagrange interpolation constant on triangular finite elements X Liu, C You Applied Mathematics and Computation 319, 693-701, 2018 | 4 | 2018 |

Global stiffness structural optimization for 3D printing under unknown loads YT Wang, Y Liu, X Liu, Z Yang, DM Yan, L Liu | 4 | 2016 |

Verified eigenvalue evaluation for Laplace operator on arbitrary polygonal domain (Mathematical foundation and development of algorithms for scientific computing) X Liu, S Oishi 京都大学数理解析研究所, 2011 | 4 | 2011 |

血管的三维重建 徐晋， 刘雪峰， 柏容刚 工程数学学报 19 (F02), 35-40, 2002 | 3 | 2002 |

Estimation of error constants appearing in non-conforming linear triangular finite element X Liu, F Kikuchi Proceedings of APCOM, 0 | 3 | |