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.
• I am currently accepting new PhD students for Spring 2024 and Fall 2024. If you are interested in discontinuous Galerkin methods, space-time finite element methods, and/or preconditioning and looking for a supervisor, you can reach out to me.

PUBLICATIONS

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

• A. Cesmelioglu, J. J. Lee, S. Rhebergen and D. Tabaku, A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem. Submitted 2023. 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
• 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. Submitted 2023. 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. Submitted 2023. Preprint
• S. Rhebergen and B.S. Southworth, An algebraic preconditioner for the exactly divergence-free discontinuous Galerkin method for Stokes. Submitted 2022. 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 (2023). Accepted for publication. 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