SANDER RHEBERGEN
Associate Professor
Department of Applied Mathematics
University of Waterloo


RESEARCH INTERESTS

Research interests include the numerical solution of partial differential equations with applications in fluid mechanics, specifically, discontinuous Galerkin methods, space-time finite element methods, and fast iterative solvers.



STUDENTS

Supervision of PhD, Master, and undergraduate students in the Applied Mathematics program and Master students in the Computational Mathematics program that have an interest in the numerical solution of partial differential equations.



PUBLICATIONS

See also ORCiD and Google Scholar.

  1. A. D. Lindsay, S. Rhebergen and B. S. Southworth, Preconditioning a hybridizable discontinuous Galerkin method for Navier-Stokes at high Reynolds number. Submitted 2025.  Preprint
  2. E. Henriquez, J. J. Lee and S. Rhebergen, Preconditioning of a hybridizable discontinuous Galerkin method for Biot’s consolidation model. Submitted 2025.  Preprint
  3. Y. Wang and S. Rhebergen, A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem. Submitted 2024. Preprint
  4. A. Fazeli, S. Rhebergen and N. M. Abukhdeir, Laminar dispersion force effects on two-fluid modelling and simulation of bubble column hydrodynamics, International Journal of Multiphase Flow 197 (2026), 105590.
  5. A. Cesmelioglu, M. Kuchta, J. J. Lee and S. Rhebergen, A coupled HDG/DG method for porous media with conducting/sealing faults, Computers and Mathematics with Applications 200 (2025), pp. 331-348.  Preprint
  6. E. Henriquez, J. J. Lee and S. Rhebergen, Parameter-robust preconditioning for hybridizable symmetric discretizations, SIAM Journal on Scientific Computing 47/6 (2025), pp. A3212-A3238. Preprint
  7. Y. Wang and S. Rhebergen, Space-time hybridizable discontinuous Galerkin method for advection-diffusion: The advection-dominated regime, IMA Journal of Numerical Analysis (2025). Accepted for publication. Preprint
  8. S. Rhebergen and B. S. Southworth, An algebraic preconditioner for the exactly divergence-free discontinuous Galerkin method for Stokes, Numerical Methods for Partial Differential Equations 41/2 (2025). Preprint
  9. A. Cesmelioglu, J. J. Lee and S. Rhebergen, A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes/Biot problem, ESAIM: Mathematical Modelling and Numerical Analysis 58 (2024), pp. 1461-1495. Preprint
  10. A. Cesmelioglu, J. J. Lee, S. Rhebergen and D. Tabaku, A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem, Computers and Mathematics with Applications 164 (2024), pp. 180-195. Preprint
  11. A. Cesmelioglu, J.J. Lee and S. Rhebergen, A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem, ESAIM: Mathematical Modelling and Numerical Analysis 58 (2024), pp. 273-302. Preprint
  12. J. P. Dean, S. Rhebergen and G. N. Wells, Design and analysis of a hybridized discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells, Computer Methods in Applied Mechanics and Engineering 417B (2023), 116493. Preprint
  13. A. Cesmelioglu, J.J. Lee and S. Rhebergen, Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model. Journal of Scientific Computing 97:60 (2023). Preprint
  14. A. Cesmelioglu, J.J. Lee and S. Rhebergen, Hybridizable discontinuous Galerkin methods for the coupled Stokes-Biot problem. Computers and Mathematics with Applications 144 (2023), pp. 12-33. Preprint
  15. A. Cesmelioglu, D.D. Pham and S. Rhebergen, A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2023), pp. 1257-1296. Preprint
  16. A. Cesmelioglu and S. Rhebergen, A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem, Journal of Computational and Applied Mathematics, 422 (2023), 114923. Preprint
  17. K.L.A. Kirk, T. Horvath and S. Rhebergen, Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier-Stokes equations, Mathematics of Computation, 92/340 (2023), pp. 525-556. Preprint
  18. K.L.A. Kirk, A. Cesmelioglu and S. Rhebergen, Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier-Stokes equations, Mathematics of Computation, 92/339 (2023), pp. 147-174. Preprint
  19. G. Sosa Jones and S. Rhebergen, An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows, Computers & Fluids, 246 (2022), 105625. Preprint
  20. T. Horvath and S. Rhebergen, A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction, International Journal for Numerical Methods in Fluids, 94/11 (2022), pp. 1784-1809. Preprint
  21. A. Baier-Reinio, S. Rhebergen and G. N. Wells, Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity, Journal of Scientific Computing, 92:51 (2022). Preprint
  22. S. Rhebergen and G.N. Wells, Preconditioning for a pressure-robust HDG discretization of the Stokes equations, SIAM Journal on Scientific Computing, 44/1 (2022), pp. A583-A604. Preprint
  23. A. Cesmelioglu and S. Rhebergen, A compatible embedded-hybridized discontinuous Galerkin method for the Stokes-Darcy-transport problem, Communications on Applied Mathematics and Computation, 4 (2022), pp. 293-318. Preprint
  24. A.A. Sivas, B.S. Southworth and S. Rhebergen, AIR algebraic multigrid for a space-time hybridizable discontinuous Galerkin discretization of advection(-diffusion), SIAM Journal on Scientific Computing, 43/5 (2021), pp. A3393-A3416. Preprint
  25. Y. He, S. Rhebergen and H. De Sterck, Local Fourier analysis of multigrid for hybridized and embedded discontinuous Galerkin methods, SIAM Journal on Scientific Computing, 43/5 (2021), pp. S612-S636. Preprint
  26. R. Oyarzúa, S. Rhebergen, M. Solano and P. Zúñiga, Error analysis of a conforming and locking-free four-field formulation for the stationary Biot's model, ESAIM: Mathematical Modelling and Numerical Analysis, 55 (2021), S475-S506. Preprint
  27. G. Sosa Jones, J.J. Lee and S. Rhebergen, A space-time hybridizable discontinuous Galerkin method for linear free-surface waves, Journal of Scientific Computing, 85:61 (2020). Preprint
  28. P.L. Lederer and S. Rhebergen, A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators, SIAM Journal on Numerical Analysis, 58/5 (2020), pp. 2915-2933. Preprint
  29. T. Horvath and S. Rhebergen, An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains, Journal of Computational Physics, 417 (2020), 109577. Preprint
  30. C. Meaney, S. Rhebergen and M. Kohandel, In silico analysis of hypoxia activated prodrugs in combination with anti angiogenic therapy through nanocell delivery, PLOS Computational Biology, 16/5 (2020), pp. 1-21.
  31. B.S. Southworth, A.A. Sivas and S. Rhebergen, On fixed-point, Krylov, and 2x2 block preconditioners for nonsymmetric problems, SIAM Journal on Matrix Analysis and Applications, 41/2 (2020), pp. 871-900. Preprint
  32. A. Cesmelioglu, S. Rhebergen and G.N. Wells, An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system, Journal of Computational and Applied Mathematics, 367 (2020), 112476. Preprint
  33. S. Rhebergen and G.N. Wells, An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations, Computer Methods in Applied Mechanics and Engineering, 358 (2020), 112619. Preprint
  34. K.L.A. Kirk and S. Rhebergen, Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations, Journal of Scientific Computing, 81/2 (2019), pp 881-897. Preprint
  35. K.L.A. Kirk, T. Horvath, A. Cesmelioglu and S. Rhebergen, Analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem on time-dependent domains, SIAM Journal on Numerical Analysis, 57/4 (2019), pp. 1677-1696. Preprint
  36. T. Horvath and S. Rhebergen, A locally conservative and energy-stable finite element method for the Navier-Stokes problem on time-dependent domains, International Journal for Numerical Methods in Fluids, 89/12 (2019), pp 519-532. Preprint
  37. S. Rhebergen and G.N. Wells, Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations, Journal of Scientific Computing, 77/3 (2018), pp 1936-1952. Preprint
  38. S. Rhebergen and G.N. Wells, A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field, Journal of Scientific Computing, 76/3 (2018), pp 1484-1501. Preprint
  39. S. Rhebergen and G.N. Wells, Analysis of a hybridized/interface stabilized finite element method for the Stokes equations, SIAM Journal on Numerical Analysis, 55/4 (2017), pp. 1982-2003. Preprint
  40. L. Alisic, S. Rhebergen, J.F. Rudge, R.F. Katz and G.N. Wells, Torsion of a cylinder of partially molten mantle with a spherical inclusion: theory and simulation, Geochemistry, Geophysics, Geosystems, 17/1 (2016), pp. 143-161. Preprint
  41. S. Rhebergen, G.N. Wells, A.J. Wathen and R.F. Katz, Three-field block-preconditioners for models of coupled magma/mantle dynamics, SIAM Journal on Scientific Computing, 37/5 (2015), pp. A2270-A2294. Preprint
  42. S. Rhebergen, G.N. Wells, R.F. Katz and A.J. Wathen, Analysis of block-preconditioners for models of coupled magma/mantle dynamics, SIAM Journal on Scientific Computing, 36/4 (2014), pp. A1960-A1977. Preprint
  43. L. Alisic, J.F. Rudge, R.F. Katz, G.N. Wells and S. Rhebergen, Compaction around a rigid, circular inclusion in partially molten rock, Journal of Geophysical Research: Solid Earth, 119/7 (2014), pp. 5903-5920. Preprint
  44. S. Rhebergen, B. Cockburn and J.J.W. van der Vegt, A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations, Journal of Computational Physics, 233 (2013), pp. 339-358. Preprint
  45. S. Rhebergen and B. Cockburn, Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes, In C.A. de Moura and C.S. Kubrusly, editors, The Courant-Friedrichs-Lewy (CFL) condition, 80 years after its discovery, pp. 45-63, Birkhauser Science, 2013.
  46. J.J.W. van der Vegt and S. Rhebergen, hp- Multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part I. Multilevel analysis, Journal of Computational Physics, 231/22 (2012), pp. 7537-7563. Preprint
  47. J.J.W. van der Vegt and S. Rhebergen, hp- Multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II. Optimization of the Runge-Kutta smoother, Journal of Computational Physics, 231/22 (2012), pp. 7564-7583. Preprint
  48. S. Rhebergen and B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, Journal of Computational Physics, 231/11 (2012), pp. 4185-4204.
  49. S. Rhebergen, J.J.W. van der Vegt and H. van der Ven, Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows, In N. Kroll, H. Bieler, H. Deconinck, V. Couallier, H. Van der Ven and K. Sorensen, editors, ADIGMA - A European initiative on the development of adaptive higher-order variational methods for aerospace applications, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 113, pp. 257-269, 2010. Preprint
  50. S. Rhebergen, O. Bokhove and J.J.W. van der Vegt, Discontinuous Galerkin finite element method for shallow two-phase flows, Computer Methods in Applied Mechanics and Engineering, 198/5-8 (2009), pp. 819-830. Preprint
  51. P.A. Tassi, S. Rhebergen, C.A. Vionnet and O. Bokhove, A discontinuous Galerkin finite element model for river bed evolution under shallow flows, Computer Methods in Applied Mechanics and Engineering, 197/33-40 (2008), pp. 2930-2947. Preprint
  52. S. Rhebergen, O. Bokhove and J.J.W. van der Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, Journal of Computational Physics, 227/3 (2008), pp. 1887-1922. Preprint