{"id":41,"date":"2019-07-31T14:52:08","date_gmt":"2019-07-31T18:52:08","guid":{"rendered":"http:\/\/sites.nd.edu\/gfu\/?page_id=41"},"modified":"2025-07-02T10:12:40","modified_gmt":"2025-07-02T14:12:40","slug":"publications","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/gfu\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"

[Submitted Manuscripts]<\/p>\n

    \n
  1. \nG. Fu<\/a>, B. Keith<\/a>, and R. Masri<\/a>*, A locally-conservative proximal Galerkin method for pointwise bound constraints. submitted to Math. Comp.<\/i> [.pdf]<\/a><\/li>\n<\/ol>\n

    [Published Journal Articles]<\/p>\n

      \n
    1. \nG. Fu<\/a>, M. Neunteufel<\/a>, J. Schoeberl<\/a>, and A. Zdunek, A four-field mixed formulation for incompressible finite elasticity. Comput. Methods Appl. Mech. Engrg. 444 (2025), 118082.<\/i>[http]<\/a>[.pdf]<\/a>\n<\/li>\n
    2. \nA. Vijaywargiya, G. Fu<\/a>, S. Osher<\/a>, and W. Li<\/a>, Efficient Computation of Mean field Control based Barycenters from Reaction-Diffusion Systems. J. Comput. Phys. 527(2025), 113772.<\/i> [http]<\/a>[.pdf]<\/a>\n<\/li>\n
    3. \nG. Fu<\/a>, H. Ji<\/a>, W. Pazner<\/a>, and W. Li<\/a>. Mean field control of droplet dynamics with high order finite element computations. J. Fluid Mech., 999 (2024), A76. <\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    4. \nG. Fu<\/a> and W. Kuang<\/a>. hp-Multigrid preconditioner for a divergence-conforming HDG scheme for the
      \nincompressible flow problems. J. Sci. Comput., 100, 16 (2024)<\/i>       [http]<\/a>[.pdf]<\/a><\/li>\n
    5. \nG. Fu<\/a> and A. Vijaywargiya. Two finite element approaches for the porous medium equation that are positivity preserving and energy stable. J. Sci. Comput., 100, 86 (2024) <\/i> [http]<\/a> [.pdf]<\/a><\/li>\n
    6. \nG. Fu<\/a>, S. Osher<\/a>, W. Pazner<\/a>, and W. Li<\/a>. Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. J. Comput. Phys. 508 (2024), 112994. <\/i> [http]<\/a> [.pdf]<\/a><\/li>\n
    7. \nG. Fu<\/a> and W. Kuang<\/a>. Optimal Geometric Multigrid Preconditioners for HDG-P0 Schemes for the reaction-diffusion equation and the Generalized Stokes equations. ESAIM Math. Model. Numer. Anal., 57(2023), pp. 1553-1587.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    8. \nG. Fu<\/a>, S. Osher<\/a>, and W. Li<\/a>. High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems. J. Comput. Phys., 491 (2023), 112375.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    9. \nG. Fu<\/a> and C. Liu<\/a>. High-order variational Lagrangian schemes for compressible fluids. J. Comput. Phys., 491 (2023), 112398.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    10. \nG. Fu<\/a>, S. Liu<\/a>, S. Osher<\/a>, and W. Li<\/a>. High order computation of optimal transport, mean field planning, and potential mean field games. J. Comput. Phys., 491 (2023), 112346.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    11. \nG. Fu<\/a> and Y. Yang<\/a>. A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous medias. Adv. Water Resour., 173(2023), 104390.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    12. \nM. Buka\u010d<\/a>, G. Fu<\/a>, A. Seboldt, and C. Trenchea<\/a>. Time-adaptive partitioned method for fluid-structure interaction problems with thick structures. J. Comput. Phys., 473(2023), 111708.<\/i> [http]<\/a><\/li>\n
    13. \nG. Fu<\/a> and W. Kuang<\/a>. Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations. IMA J. Numer. Anal., 43(2023), pp. 1718-1741.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    14. \nG. Fu<\/a>. Monolithic and partitioned finite element schemes for FSI based on an ALE divergence-free HDG fluid solver and a TDNNS structural solver. Int. J. Numer. Anal. Model., 20(2023), pp. 267-312.<\/i> [.pdf]<\/a><\/li>\n
    15. \nG. Fu<\/a>. A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation. J. Sci. Comput., (2022), 92:86.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    16. \nG. Fu<\/a> and Z. Xu<\/a>. High-order space\u2013time finite element methods for the Poisson\u2013Nernst\u2013Planck equations: Positivity and unconditional energy stability. Comput. Methods Appl. Mech. Engrg., 395 (2022), 115031.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    17. \nW. Guo, C. Dun, C. Yu, X. Song, F. Yang, W. Kuang, Y. Xie, S. Li, Z. Wang, J. Yu, G. Fu, J.
      \nGuo, M. A. Marcus, J. J. Urban, Q. Zhang, and J. Qiu. Mismatching integration-enabled strains and
      \ndefects engineering in LDH microstructure for high-rate and long-life charge storage . Nature Commu-
      \nnications, 13 (2022), Article number: 1409.<\/i>      [http]<\/a>\n<\/li>\n
    18. \nG. Fu<\/a> and Y. Yang<\/a>. A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media. Adv. Water Resour., 161 (2022), 104129.<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    19. \nG. Fu<\/a> and W. Kuang<\/a>. A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model. SIAM J. Numer. Anal., 60 (2022), pp. 631-658<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    20. \n G. Fu<\/a>, and D. Han<\/a>. A linear second-order in time unconditionally energy stable finite element scheme for a Cahn-Hilliard phase-field model for two-phase incompressible flow of variable densities. Comput. Methods Appl. Mech. Engrg., 387 (2021), 114186. <\/i>[http]<\/a>\n <\/li>\n
    21. \nG. Fu<\/a>, C. Lehrenfeld<\/a>, A. Linke<\/a>, T. Streckenbach<\/a>. Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity. J. Sci. Comput. (2021), 86:61.<\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    22. \nL. Feng<\/a>, G. Fu<\/a>, and Z. Wang<\/a>. A FOM\/ROM Hybrid Approach for Accelerating Numerical Simulations. J. Sci. Comput. (2021) 89:61. <\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    23. \nG. Fu<\/a>. Uniform auxiliary space preconditioning for HDG methods for elliptic operators with a parameter dependent low order term. SIAM J. Sci. Comput. 43 (2021), pp. A3912-A3937<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    24. \nG. Fu<\/a> and Z. Wang<\/a>. POD-(H)DG Method for Incompressible Flow Simulations. J. Sci. Comput. (2020), 85:24.<\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    25. \nG. Fu<\/a>. A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow. J. Comput. Phys. 419(2020), 109671.<\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    26. \nG. Fu<\/a>. Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces. Comput. Methods Appl. Mech. Engrg. 367(2020), 113158.<\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    27. \nG. Fu<\/a>, J. Guzman<\/a>, and M. Neilan<\/a>. Exact smooth piecewise polynomial sequences on Alfeld splits. Math. Comp., 89(2020), pp. 1059-1091<\/i> [http]<\/a>[.pdf]<\/a><\/li>\n
    28. \nG. Chen<\/a>,G. Fu<\/a>, J.R. Singler<\/a>, and Y. Zhang<\/a>. A class of embedded DG methods for Dirichlet boundary control of convection diffusion PDEs. J. Sci. Comput. 81(2019), pp. 623-648.<\/i>[http]<\/a>[.pdf]<\/a><\/li>\n
    29. G. Fu<\/a> and C.-W. Shu<\/a>. Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. J. Comput. Phys., 394(2019), pp. 329-363<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    30. \nG. Fu<\/a>. An explicit divergence-free DG method for incompressible magnetohydrodynamics.
      \nJ. Sci. Comput., 79(2019), pp. 1737-1752. <\/i>      [http]<\/a>, [.pdf]<\/a><\/li>\n
    31. \nG. Fu<\/a>. An explicit divergence-free DG method for incompressible flow. Comput. Methods Appl. Mech. Engrg., 345(2019), pp. 502-517.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    32. \nM. Ainsworth<\/a> and G. Fu<\/a>. Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation. J. Sci. Comput., 79(2019), pp. 209-226.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    33. \nG. Fu<\/a>. A high-order HDG method for the Biot’s consolidation model. Comput. Math. Appl., 77 (2019), pp . 237-252.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    34. \nG. Fu<\/a> and C.-W. Shu<\/a>. An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation. J. Comput. Appl. Math., 349 (2019), pp. 41-51.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    35. \nG. Fu<\/a>, Y. Jin<\/a>, and W. Qiu<\/a>. Parameter-free superconvergent H(div)-conforming HDG methods for the Brinkman equations. IMA J. Numer. Anal., 39(2019), pp. 957-982.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    36. \nB. Cockburn<\/a>, G. Fu<\/a>, and W. Qiu<\/a>. Discrete H1-inequalities for spaces admitting M-decompositions. SIAM J. Numer. Anal., 56(2018), pp. 3407-3429.<\/i>[http]<\/a>, [.pdf]<\/a><\/li>\n
    37. \nM. Ainsworth<\/a> and G. Fu<\/a>. Bernstein-Bezier Bases for Tetrahedral Finite Elements. Comput. Methods Appl. Mech. Engrg., 340(2018), pp. 178-201.<\/i>[http]<\/a>, [.pdf]<\/a><\/li>\n
    38. \nM. Ainsworth<\/a> and G. Fu<\/a>. Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. J. Sci. Comput., 77(2018), pp. 443-466.<\/i>[http]<\/a>, [.pdf]<\/a><\/li>\n
    39. \nG. Fu<\/a> and C. Lehrenfeld<\/a>. A Strongly Conservative Hybrid DG\/Mixed FEM for the Coupling of Stokes and Darcy Flow. J. Sci. Comput., 77 (2018), pp. 1605-1620.<\/i>[http]<\/a><\/li>\n
    40. \nB. Cockburn<\/a> and G. Fu<\/a>. Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity. IMA J. Numer. Anal., 38(2018), pp. 566-604.<\/i>[http]<\/a>, [.pdf]<\/a><\/li>\n
    41. \nM. Ainsworth<\/a> and G. Fu<\/a>. A lowest-order composite finite element exact sequence on pyramids. Comput. Methods Appl. Mech. Engrg., 324(2017), pp. 110-127.<\/i>[http]<\/a>, [.pdf]<\/a><\/li>\n
    42. \nG. Fu<\/a> and C.-W. Shu<\/a>. A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. J. Comput. Phys., 347(2017), pp. 305-327.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    43. \nG. Fu<\/a> and C.-W. Shu<\/a>. Analysis of an embedded discontinuous Galerkin method with implicit-explicit time-marching for convection-diffusion problems. Int. J. Numer. Anal. Model., 14(2017), pp. 477-499.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    44. \nB. Cockburn<\/a> and G. Fu<\/a>. A systematic construction of finite element commuting exact sequences. SIAM J. Numer. Anal., 55(2017), pp. 1650-1688.<\/i> [http]<\/a>, [.pdf]<\/a><\/li>\n
    45. \nB. Cockburn<\/a>, G. Fu<\/a>, and W. Qiu<\/a>. A note on the devising of superconvergent HDG methods for the Stokes flow by M-decompositions. IMA J. Numer. Anal., 37(2017), pp. 730-749<\/i> [http]<\/a><\/li>\n
    46. \nB. Cockburn<\/a> and G. Fu<\/a>. Superconvergence by M-decompositions. Part III: Construction of three-dimensional finite elements. ESAIM: Math. Model. Numer. Anal., 51(2017), pp. 365-398.<\/i> [http]<\/a><\/li>\n
    47. \nB. Cockburn<\/a> and G. Fu<\/a>. Superconvergence by M-decompositions. Part II: Construction of two-dimensional finite elements. ESAIM: Math. Model. Numer. Anal., 51(2017), pp. 165-186.<\/i>[http]<\/a><\/li>\n
    48. \nB. Cockburn<\/a>, G. Fu<\/a>, and F.-J. Sayas<\/a>. Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. Math. Comp., 86(2017), pp. 1609-1641.<\/i>[http]<\/a><\/li>\n
    49. \nE. Chung<\/a>, B. Cockburn<\/a>, and G. Fu<\/a>. The staggered DG method is the limit of a hybridizable DG method. Part II: the Stokes system. J. Sci. Comput., 66(2016), pp. 870-887. <\/i>[http]<\/a><\/li>\n
    50. \nG. Fu<\/a>, B. Cockburn<\/a>, and H. Stolarski<\/a>. Analysis of an HDG method for linear elasticity. Internat. J. Numer. Methods Engrg., 102(2015),pp. 551-575. <\/i> [http] <\/a><\/li>\n
    51. \nG. Fu<\/a>, W. Qiu<\/a>, and W. Zhang<\/a>. An analysis of HDG methods for convection dominated diffusion problems. ESAIM: Math. Model. Numer. Anal., 49(2015), pp. 225-256. <\/i>[http]<\/a><\/li>\n
    52. \nH. Chen<\/a>, G. Fu<\/a>, J. Li<\/a>, and W. Qiu<\/a>. First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems. Comput. Math. Appl., 68(2014), pp. 1635-1652. <\/i> [http]<\/a><\/li>\n
    53. \nE. Chung<\/a>, B. Cockburn<\/a>, and G. Fu<\/a>. The staggered DG method is the limit of a hybridizable DG method. SIAM J. Numer. Anal., 52(2014), pp. 915-932. <\/i> [http] <\/a><\/li>\n<\/ol>\n

      [Thesis]<\/p>\n

        \n
      1. \nG. Fu<\/a>. Devising superconvergent HDG methods by M-decompositions. Ph.D. Thesis, University of Minnesota Twin Cities, 2016.<\/i>[http]<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

        [Submitted Manuscripts] G. Fu, B. Keith, and R. Masri*, A locally-conservative proximal Galerkin method for pointwise bound constraints. submitted to Math. Comp. [.pdf] [Published Journal Articles] G. Fu, M. Neunteufel, J. Schoeberl, and A. Zdunek, A four-field mixed formulation for incompressible finite elasticity. Comput. Methods Appl. Mech. Engrg. 444 (2025), 118082.[http][.pdf] A. Vijaywargiya, G. Fu, […]<\/p>\n","protected":false},"author":3458,"featured_media":0,"parent":0,"menu_order":-3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-41","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/pages\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/users\/3458"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/comments?post=41"}],"version-history":[{"count":90,"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":424,"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/pages\/41\/revisions\/424"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/gfu\/wp-json\/wp\/v2\/media?parent=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}