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Publications

[Submitted articles]

  1. G. Fu and A. Vijaywargiya. Two finite element approaches for the porous medium equation that are positivity preserving and energy stable. submitted to J. Sci. Comput. [.pdf]
  2. G. Fu and W. Kuang. $hp$-Multigrid preconditioner for a divergence-conforming HDG scheme for the
    incompressible flow problems. submitted to J. Sci. Comput. [.pdf]
  3. G. Fu, S. Osher, W. Pazner, and W. Li. Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. submitted to J. Comput. Phys. [.pdf]
  4. G. Fu, H. Ji, W. Pazner, and W. Li. Mean field control of droplet dynamics with high order finite element computations. submitted to J. Fluid Mech. [.pdf]

[Accepted articles]

  1. G. Fu and W. Kuang. 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. [http][.pdf]
  2. G. Fu, S. Osher, and W. Li. High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems. J. Comput. Phys., 491 (2023), 112375. [http][.pdf]
  3. G. Fu and C. Liu. High-order variational Lagrangian schemes for compressible fluids. J. Comput. Phys., 491 (2023), 112398. [http][.pdf]
  4. G. Fu, S. Liu, S. Osher, and W. Li. High order computation of optimal transport, mean field planning, and potential mean field games. J. Comput. Phys., 491 (2023), 112346. [http][.pdf]
  5. G. Fu and Y. Yang. A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous medias. Adv. Water Resour., 173(2023), 104390. [http][.pdf]
  6. M. Bukač, G. Fu, A. Seboldt, and C. Trenchea. Time-adaptive partitioned method for fluid-structure interaction problems with thick structures. J. Comput. Phys., 473(2023), 111708. [http]
  7. G. Fu and W. Kuang. 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. [http][.pdf]
  8. G. Fu. 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. [.pdf]
  9. G. Fu. 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. [http][.pdf]
  10. G. Fu and Z. Xu. High-order space–time finite element methods for the Poisson–Nernst–Planck equations: Positivity and unconditional energy stability. Comput. Methods Appl. Mech. Engrg., 395 (2022), 115031. [http][.pdf]
  11. G. Fu and Y. Yang. A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media. Adv. Water Resour., 161 (2022), 104129. [http][.pdf]
  12. G. Fu and W. Kuang. A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model. SIAM J. Numer. Anal., 60 (2022), pp. 631-658 [http][.pdf]
  13. G. Fu, and D. Han. 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. [http]
  14. L. Feng, G. Fu, and Z. Wang. A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations. J. Sci. Comput. (2021) 89:61. [http][.pdf]
  15. G. Fu. 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 [http][.pdf]
  16. G. Fu, C. Lehrenfeld, A. Linke, T. Streckenbach. Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity. J. Sci. Comput. (2021), 86:61.[http][.pdf]
  17. G. Fu and Z. Wang. POD-(H)DG Method for Incompressible Flow Simulations. J. Sci. Comput. (2020), 85:24.[http][.pdf]
  18. G. Fu. A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow. J. Comput. Phys. 419(2020), 109671.[http][.pdf]
  19. G. Fu. Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces. Comput. Methods Appl. Mech. Engrg. 367(2020), 113158.[http][.pdf]
  20. G. Fu, J. Guzman, and M. Neilan. Exact smooth piecewise polynomial sequences on Alfeld splits. Math. Comp., 89(2020), pp. 1059-1091 [http][.pdf]
  21. G. Chen,G. Fu, J.R. Singler, and Y. Zhang. A class of embedded DG methods for Dirichlet boundary control of convection diffusion PDEs. J. Sci. Comput. 81(2019), pp. 623-648.[http][.pdf]
  22. G. Fu and C.-W. Shu. Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. J. Comput. Phys., 394(2019), pp. 329-363 [http], [.pdf]
  23. G. Fu. An explicit divergence-free DG method for incompressible magnetohydrodynamics.
    J. Sci. Comput., 79(2019), pp. 1737-1752.     [http], [.pdf]
  24. G. Fu. An explicit divergence-free DG method for incompressible flow. Comput. Methods Appl. Mech. Engrg., 345(2019), pp. 502-517. [http], [.pdf]
  25. B. Cockburn, G. Fu, and W. Qiu. Discrete H1-inequalities for spaces admitting M-decompositions. SIAM J. Numer. Anal., 56(2018), pp. 3407-3429.[http], [.pdf]
  26. M. Ainsworth and G. Fu. Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation. J. Sci. Comput., 79(2019), pp. 209-226. [http], [.pdf]
  27. G. Fu and C.-W. Shu. An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation. J. Comput. Appl. Math., 349 (2019), pp. 41-51. [http], [.pdf]
  28. G. Fu. A high-order HDG method for the Biot’s consolidation model. Comput. Math. Appl., 77 (2019), pp . 237-252. [http], [.pdf]
  29. M. Ainsworth and G. Fu. Bernstein-Bezier Bases for Tetrahedral Finite Elements. Comput. Methods Appl. Mech. Engrg., 340(2018), pp. 178-201.[http], [.pdf]
  30. M. Ainsworth and G. Fu. Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. J. Sci. Comput., 77(2018), pp. 443-466.[http], [.pdf]
  31. G. Fu and C. Lehrenfeld. A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow. J. Sci. Comput., 77 (2018), pp. 1605-1620.[http]
  32. G. Fu, Y. Jin, and W. Qiu. Parameter-free superconvergent H(div)-conforming HDG methods for the Brinkman equations. IMA J. Numer. Anal., 39(2019), pp. 957-982. [http], [.pdf]
  33. B. Cockburn and G. Fu. Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity. IMA J. Numer. Anal., 38(2018), pp. 566-604.[http], [.pdf]
  34. M. Ainsworth and G. Fu. A lowest-order composite finite element exact sequence on pyramids. Comput. Methods Appl. Mech. Engrg., 324(2017), pp. 110-127.[http], [.pdf]
  35. G. Fu and C.-W. Shu. A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws. J. Comput. Phys., 347(2017), pp. 305-327. [http], [.pdf]
  36. G. Fu and C.-W. Shu. 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. [http], [.pdf]
  37. B. Cockburn and G. Fu. A systematic construction of finite element commuting exact sequences. SIAM J. Numer. Anal., 55(2017), pp. 1650-1688. [http], [.pdf]
  38. B. Cockburn, G. Fu, and W. Qiu. 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 [http]
  39. B. Cockburn and G. Fu. Superconvergence by M-decompositions. Part III: Construction of three-dimensional finite elements. ESAIM: Math. Model. Numer. Anal., 51(2017), pp. 365-398. [http]
  40. B. Cockburn and G. Fu. Superconvergence by M-decompositions. Part II: Construction of two-dimensional finite elements. ESAIM: Math. Model. Numer. Anal., 51(2017), pp. 165-186.[http]
  41. B. Cockburn, G. Fu, and F.-J. Sayas. Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion. Math. Comp., 86(2017), pp. 1609-1641.[http]
  42. E. Chung, B. Cockburn, and G. Fu. 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. [http]
  43. G. Fu, B. Cockburn, and H. Stolarski. Analysis of an HDG method for linear elasticity. Internat. J. Numer. Methods Engrg., 102(2015),pp. 551-575. [http]
  44. G. Fu, W. Qiu, and W. Zhang. An analysis of HDG methods for convection dominated diffusion problems. ESAIM: Math. Model. Numer. Anal., 49(2015), pp. 225-256. [http]
  45. H. Chen, G. Fu, J. Li, and W. Qiu. First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems. Comput. Math. Appl., 68(2014), pp. 1635-1652. [http]
  46. E. Chung, B. Cockburn, and G. Fu. The staggered DG method is the limit of a hybridizable DG method. SIAM J. Numer. Anal., 52(2014), pp. 915-932. [http]

[Thesis]

  1. G. Fu. Devising superconvergent HDG methods by M-decompositions. Ph.D. Thesis, University of Minnesota Twin Cities, 2016.[http]