| 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 | 106 | 2013 |
| A framework of verified eigenvalue bounds for self-adjoint differential operators X Liu Applied Mathematics and Computation 267, 341-355, 2015 | 87 | 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 | 70 | 2007 |
| 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 | 59 | 2010 |
| Determination of the Babuska-Aziz constant for the linear triangular finite element F Kikuchi, L Xuefeng Japan Journal of Industrial and Applied Mathematics 23, 75-82, 2006 | 49 | 2006 |
| 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 | 37 | 2013 |
| Guaranteed eigenvalue bounds for the Steklov eigenvalue problem C You, H Xie, X Liu SIAM Journal on Numerical Analysis 57 (3), 1395-1410, 2019 | 25 | 2019 |
| Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation K Tanaka, A Takayasu, X Liu, S Oishi Japan Journal of Industrial and Applied Mathematics 31, 665–679, 2014 | 23 | 2014 |
| 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, 335-354, 2018 | 20 | 2018 |
| Optimal estimation for the Fujino–Morley interpolation error constants SK Liao, YC Shu, X Liu Japan Journal of Industrial and Applied Mathematics 36, 521-542, 2019 | 17 | 2019 |
| Explicit bound for quadratic Lagrange interpolation constant on triangular finite elements X Liu, C You Applied Mathematics and Computation 319, 693-701, 2018 | 16 | 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 | 16 | 2014 |
| Guaranteed high-precision estimation for P 0 interpolation constants on triangular finite elements X Liu, S Oishi Japan Journal of Industrial and Applied Mathematics 30, 635-652, 2013 | 16 | 2013 |
| Explicit finite element error estimates for nonhomogeneous Neumann problems Q Li, X Liu Applications of Mathematics 63 (3), 367-379, 2018 | 12 | 2018 |
| High-precision eigenvalue bound for the Laplacian with singularities X Liu, T Okayama, S Oishi Computer Mathematics: 9th Asian Symposium (ASCM2009), Fukuoka, December 2009 …, 2014 | 10 | 2014 |
| Global stiffness structural optimization for 3D printing under unknown loads TY Wang, YLX Liu, Z Yang, D Yan, L Liu Journal of Computer Graphics Techniques Vol 5 (3), 2016 | 8 | 2016 |
| Fully computable a posteriori error bounds for eigenfunctions X Liu, T Vejchodský Numerische Mathematik 152 (1), 183-221, 2022 | 7 | 2022 |
| A subdivision scheme for volumetric models G Mustafa, L Xuefeng Applied Mathematics-A Journal of Chinese Universities 20, 213-224, 2005 | 7 | 2005 |
| Explicit estimation of error constants appearing in non-conforming linear triangular finite element method X Liu, F Kikuchi Applications of Mathematics 63, 381-397, 2018 | 6 | 2018 |
| Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms X Liu Journal of Computational and Applied Mathematics 371, 112666, 2020 | 5 | 2020 |
Akitoshi TakayasuUniversity of TsukubaVerified email at risk.tsukuba.ac.jp
