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Hengguang Li

WayneState 




Journal publications
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  1. Bokai Zhu, Hengguang Li, and Qinghui Zhang. Extended physics-informed extreme learning machine for linear elastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering. 435:117655, 2025. [PDF]

  2. Wenbo Gong, Hengguang Li, and Qinghui Zhang. Improved enrichments and numerical integrations in SGFEM for interface problems. Journal of Computational and Applied Mathematics. 438:115540, 2024. [PDF]

  3. Hengguang Li, Peimeng Yin, and Zhimin Zhang. A C0 finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain. IMA Journal of Numerical Analysis. 43: 1779-1801, 2023. [PDF]

  4. Baiju Zhang, Hengguang Li, and Zhimin Zhang. Solving biharmonic eigenvalue problem with Navier boundary condition via Poisson solvers on non-convex domains. Journal of Scientific Computing. 92:24, 2022. [PDF]

  5. Hengguang Li and Serge Nicaise. A priori analysis of an anisotropic finite element method for elliptic equations in polyhedral domains. Computational Methods in Applied Mathematics, 21: 145-177, 2021. [PDF]

  6. Young Ju Lee and Hengguang Li. The macroelement analysis for axisymmetric Stokes equations Computers and Mathematics with Applications, 101: 1-22, 2021. [PDF]

  7. Hengguang Li, Xiang Wan, Peimeng Yin, and Lewei Zhao. Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources. Journal of Computational and Applied Mathematics, 393: 113518, 2021. [PDF]

  8. Guanghao Jin, Na Zhao, Chunmei Pei, Hengguang Li, Qingzeng Song, and Jing Yu. Solving the feature diversity problem based on multi-model scheme. Journal on Artificial Intelligence, 3: 135-143, 2021. [PDF]

  9. Hengguang Li and Xun Lu. Condition numbers of finite element methods on a class of anisotropic meshes. Applied Numerical Mathematics, 158: 22-43, 2020. [PDF].

  10. Hengguang Li and Qinghui Zhang. A meshfree finite volume method with optimal numerical integration and direct imposition of essential boundary conditions. Applied Numerical Mathematics, 153: 98-113, 2020. [PDF]

  11. Gerard Awanou, Hengguang Li, and Eric Malitz. A two-grid method for the C0 interior penalty discretization of the Monge-Ampère equation. Journal of Computational Mathematics, 38: 547-564, 2020. [PDF]

  12. Li Guo, Hengguang Li, and Qingsong Zou. Interior estimates of finite volume element methods over rectangular meshes for elliptic equations. SIAM Journal on Numerical Analysis, 57: 2246-2265, 2019. [PDF]

  13. Hengguang Li, Lin Mu, and Xiu Ye. A posteriori error estimates for the weak Galerkin finite element methods on polytopal meshes. Communications in Computational Physics, 26: 558-578, 2019. [PDF]

  14. Majid Haghi, Hengguang Li, and Reza Mollapourasl. A local radial basis function method for pricing options under the regime switching model. Journal of Scientific Computing, 79: 517-541, 2019. [PDF]

  15. Li Guo, Hengguang Li, and Yang Yang. Interior estimates of semidiscrete finite element methods for parabolic problems with distributional data. Journal of Computational Mathematics, 37: 458-474, 2019. [PDF]

  16. Hengguang Li and Serge Nicaise. Regularity and a priori error analysis on anisotropic meshes of a Dirichlet problem in polyhedral domains. Numerische Mathematik, 139: 47-92, 2018. [PDF]

  17. Hengguang Li, Lin Mu, and Xiu Ye. Interior energy estimates for the weak Galerkin finite element method. Numerische Mathematik, 139: 447-478, 2018. [PDF]

  18. Hengguang Li. An anisotropic finite element method on polyhedral domains: interpolation error analysis. Mathematics of Computation, 87: 1567-1600, 2018. [PDF]

  19. Sadreddin Mahmoodkalayeh, Xun Lu, Mohammad Ali Ansari, Hengguang Li, and Mohammadreza Nasiriavanaki. Optimization of light illumination for photoacoustic computed tomography of human infant brain. Proceedings of SPIE (international society for optics and photonics) 10494, Photons Plus Ultrasound: Imaging and Sensing, 104946U, doi: 10.1117/12.2291592, 2018. [PDF]

  20. Yu Qiao and Hengguang Li. Double layer potentials on polygons and pseudodifferential operators on Lie groupoids. Integral Equations and Operator Theory, 90: Art. 14, 26, 2018. [PDF]

  21. Reza Mollapourasl, Ali Fereshtian, Hengguang Li, and Xun Lu. RBF-PU method for pricing options under the jump diffusion model with local volatility. Journal of Computational and Applied Mathematics, 337: 98-118, 2018. [PDF]

  22. Susanne C. Brenner, Hengguang Li, and Li-yeng Sung. Multigrid methods for saddle point problems: Oseen systems. Computers & Mathematics with Applications, 74: 2056-2067, 2017. [PDF]

  23. Serge Nicaise, Hengguang Li, and Anna Mazzucato. Regularity and a priori error analysis of a Ventcel problem in polyhedral domains. Mathematical Methods in the Applied Sciences, 40: 1625-1636, 2017. [PDF]

  24. Hengguang Li. The W1p stability of the Ritz projection on graded meshes. Mathematics of Computation, 86: 49-74, 2017. [PDF]

  25. Constantin Bacuta, Hengguang Li, and Victor Nistor. Differential operators on domains with conical points: precise uniform regularity estimates. Romanian Journal of Pure and Applied Mathematics, 62: 383-411, 2017. [PDF]

  26. Guanghao Jin, Young Ju Lee and Hengguang Li. Regularity and optimal finite element methods in W1p on polygonal domains. Computers & Mathematics with Applications, 74: 2089-2105, 2017. [PDF]

  27. Hengguang Li and Qinghui Zhang. Optimal quadrilateral finite elements on polygonal domains. Journal of Scientific Computing, 70: 60-84, 2017. [PDF]

  28. Beichuan Deng, Seongho Kim, Hengguang Li, Elisabeth Heath, and Xiang Zhang. Global peak alignment for comprehensive two-dimensional gas chromatography mass spectrometry using point matching algorithms. Journal of Bioinformatics and Computational Biology, 14: 16500321-165003218, 2016. [PDF]

  29. Guanghao Jin, Hengguang Li, Qinghui Zhang, and Qingsong Zou. Linear and quadratic finite volume methods on triangular meshes for elliptic equations with singular solutions. International Journal of Numerical Analysis and Modeling, 13: 244-264, 2016. [PDF]

  30. Hengguang Li. Regularity and multigrid analysis for Laplace-type axisymmetric equations. Mathematics of Computation, 84: 1113-1144, 2015. [PDF]

  31. Hengguang Li and Jeffrey S. Ovall. A posteriori eigenvalue error estimation for the Schrödinger operator with the inverse square potential. Discrete and Continuous Dynamical Systems - Series B, 20: 1377-1391, 2015. [PDF]

  32. Hengguang Li and Jeffrey S. Ovall. A posteriori estimation of hierarchical type for the Schrödinger operator with the inverse square potential on graded meshes. Numerische Mathematik, 128: 707-740, 2014. [PDF]

  33. Susanne C. Brenner, Hengguang Li, and Li-yeng Sung. Multigrid methods for saddle point problems: Stokes and Lamé systems. Numerische Mathematik, 128: 193-216, 2014. [PDF]

  34. Gerard Awanou and Hengguang Li. Error analysis of a mixed finite element method for the Monge-Ampère equation. International Journal of Numerical Analysis and Modeling, 11: 745-761, 2014. [PDF]

  35. Eugenie Hunsicker, Hengguang Li, Victor Nistor, and Ville Uski. Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case. Numerical Methods for Partial Differential Equations, 30: 1130-1151, 2014. [PDF]

  36. Hengguang Li, Victor Nistor, and Yu Qiao. Uniform shift estimates for transmission problems and optimal rates of convergence for the parametric Finite Element Method. Numerical Analysis and Its Applications, Lecture Notes in Computer Science, 8236: 12-23, Springer-Verlag Berlin Heidelberg, 2013. [PDF]

  37. Hengguang Li and Victor Nistor. LNG_FEM: Graded meshes on domains of polygonal structures. Recent Advances in Scientific Computing and Applications, Contemporary Mathematics, 586: 239-246, American Mathematical Society, Providence, RI, 2013. [PDF]

  38. Constantin Bacuta, Hengguang Li, and Victor Nistor. Anisotropic graded meshes and quasi-optimal rates of convergence for the FEM on polyhedral domains in 3D. ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers, 9003-9014, 2012. [PDF]

  39. Young Ju Lee and Hengguang Li. Axisymmetric Stokes equations in polygonal domains: regularity and finite element approximations. Computers & Mathematics with Applications, 64: 3500-3521, 2012. [PDF]

  40. Eugenie Hunsicker, Hengguang Li, Victor Nistor, and Ville Uski. Analysis of Schrödinger operators with inverse square potentials I: regularity results in 3D. Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 55: 157 - 178, 2012. [PDF]

  41. Hengguang Li. A note on the conditioning of a class of generalized finite element methods. Applied Numerical Mathematics, 62: 754-766, 2012. [PDF]

  42. Hengguang Li. Finite element analysis for the axisymmetric Laplace operator on polygonal domains. Journal of Computational and Applied Mathematics, 235: 5155-5176, 2011. [PDF]

  43. Young Ju Lee and Hengguang Li. On stability, accuracy, and fast solvers for finite element approximations of the axisymmetric Stokes problem by Hood-Taylor elements. SIAM Journal on Numerical Analysis, 49: 668-691, 2011. [PDF]

  44. Ivo Babuška, Uday Banerjee, and Hengguang Li. The effect of numerical integration on the finite element approximation of linear functionals. Numerische Mathematik, 117: 65-88, 2011. [PDF]

  45. Hengguang Li, Anna Mazzucato, and Victor Nistor. Analysis of the Finite Element Method for transmission/mixed boundary value problems on general polygonal domains. Electronic Transactions on Numerical Analysis, 37: 41-69, 2010. [PDF]

  46. Long Chen and Hengguang Li. Superconvergence of gradient recovery schemes on graded meshes for corner singularities. Journal of Computational Mathematics, 28: 11-31, 2010. [PDF]

  47. Hengguang Li. A-priori analysis and the finite element method for a class of degenerate elliptic equations. Mathematics of Computation, 78: 713-737, 2009. [PDF]

  48. Hengguang Li and Victor Nistor. Analysis of a modified Schrödinger operator in 2D: regularity, index, and FEM. Journal of Computational and Applied Mathematics, 224: 320-338, 2009. [PDF]

  49. James Brannick, Hengguang Li, and Ludmil Zikatanov. Uniform convergence of the multigrid V-cycle on graded meshes for corner singularities. Numerical Linear Algebra with Applications, 15: 291-306, 2008. [PDF]

  50. Hengguang Li. Uniform convergence of the multigrid V-cycle on graded meshes. Proceedings of the Thirteenth Copper Mountain Conference on Multigrid Methods, 2007. [PDF]

Books:
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  • Hengguang Li. Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains. Surveys and Tutorials in the Applied Mathematical Sciences 10, Springer, 2022.
  • Hengguang Li. A Weighted Approach on Elliptic Equations with Singularities: A-priori Analysis and Numerical Methods. VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG, Saarbrücken, ISBN 978-3-639-10609-1, 2008.

Collaborators:
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    Gerard Awanou,    Ivo Babuška,    Constantin Bacuta,    Uday Banerjee,    James Brannick,    Susanne C. Brenner,    Long Chen,    Eugenie Hunsicker ,    Guanghao Jin,    Young Ju Lee,    Anna Mazzucato,    Victor Nistor,    Jeffrey S. Ovall,    Yu Qiao,    Li-yeng Sung,    Ville Uski,    Qinghui Zhang,    Ludmil Zikatanov,    Qingsong Zou