Sander Rhebergen

CONTACT

Sander Rhebergen
Department of Applied Mathematics
email: srheberg@uwaterloo.ca
office: MC 6134

RESEARCH INTERESTS

• Discontinuous Galerkin methods
• Space-time finite element methods
• Preconditioning

STUDENTS

• I supervise PhD, Master and undergraduate students in the Applied Mathematics program and Master students in the Computational Mathematics program.

PUBLICATIONS

See also ORCiD and Google Scholar.
Current and former graduate students and postdocs are indicated by (GS) and (PD), respectively.

• Y. Wang (GS) and S. Rhebergen, A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem. Submitted 2024. Preprint
• A. Cesmelioglu, J. J. Lee and S. Rhebergen, A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes/Biot problem. Submitted 2023. Preprint
• Y. Wang (GS) and S. Rhebergen, Space-time hybridizable discontinuous Galerkin method for advection-diffusion on deforming domains: The advection-dominated regime. Submitted 2023. Preprint
• 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 (2024). Accepted for publication. Preprint
• 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
• 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
• 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
• 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
• 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
• 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
• K.L.A. Kirk (GS), T.L. Horvath (PD) 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
• K.L.A. Kirk (GS), 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
• G. Sosa Jones (GS) and S. Rhebergen, An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows, Computers & Fluids, 246 (2022), 105625. Preprint
• T.L. Horvath (PD) 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
• A. Baier-Reinio (GS), 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
• 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
• 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
• A.A. Sivas (GS), 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
• Y. He (PD), 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
• R. Oyarzúa, S. Rhebergen, M. Solano and P. Zúñiga (PD), 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
• G. Sosa Jones (GS), 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
• 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
• T.L. Horvath (PD) 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
• 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.
• B.S. Southworth, A.A. Sivas (GS) 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
• 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
• 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
• K.L.A. Kirk (GS) 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
• K.L.A. Kirk (GS), T.L. Horvath (PD), 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
• T.L. Horvath (PD) 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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.
• 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
• 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
• 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.
• 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
• 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
• 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
• 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