Leo G. Rebholz, Ph.D. - Publications

Affiliations: 
2006 University of Pittsburgh, Pittsburgh, PA, United States 
Area:
Mathematics

91 high-probability publications. We are testing a new system for linking publications to authors. You can help! If you notice any inaccuracies, please sign in and mark papers as correct or incorrect matches. If you identify any major omissions or other inaccuracies in the publication list, please let us know.

Year Citation  Score
2020 Evans C, Pollock SN, Rebholz LG, Xiao M. A Proof That Anderson Acceleration Improves the Convergence Rate in Linearly Converging Fixed-Point Methods (But Not in Those Converging Quadratically) Siam Journal On Numerical Analysis. 58: 788-810. DOI: 10.1137/19M1245384  0.338
2020 Olshanskii MA, Rebholz LG. Longer time accuracy for incompressible Navier–Stokes simulations with the EMAC formulation Computer Methods in Applied Mechanics and Engineering. 372: 113369. DOI: 10.1016/J.Cma.2020.113369  0.457
2020 Rebholz LG, Viguerie A, Xiao M. Analysis of Algebraic Chorin Temam splitting for incompressible NSE and comparison to Yosida methods Journal of Computational and Applied Mathematics. 365: 112366. DOI: 10.1016/J.Cam.2019.112366  0.436
2019 Eroglu FG, Kaya S, Rebholz LG. POD-ROM for the Darcy-Brinkman equations with double-diffusive convection Journal of Numerical Mathematics. 27: 123-139. DOI: 10.1515/Jnma-2017-0122  0.498
2019 Pollock SN, Rebholz LG, Xiao M. Anderson-Accelerated Convergence of Picard Iterations for Incompressible Navier--Stokes Equations Siam Journal On Numerical Analysis. 57: 615-637. DOI: 10.1137/18M1206151  0.391
2019 Rebholz LG, Viguerie A, Xiao M. Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations Ieee Communications Magazine. 88: 1533-1557. DOI: 10.1090/Mcom/3411  0.369
2019 Larios A, Pei Y, Rebholz L. Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations Journal of Differential Equations. 266: 2435-2465. DOI: 10.1016/J.Jde.2018.08.033  0.428
2019 Linke A, Rebholz LG. Pressure-induced locking in mixed methods for time-dependent (Navier–)Stokes equations Journal of Computational Physics. 388: 350-356. DOI: 10.1016/J.Jcp.2019.03.010  0.44
2019 Zerfas C, Rebholz LG, Schneier M, Iliescu T. Continuous data assimilation reduced order models of fluid flow Computer Methods in Applied Mechanics and Engineering. 357: 112596. DOI: 10.1016/J.Cma.2019.112596  0.697
2019 Larios A, Rebholz LG, Zerfas C. Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations Computer Methods in Applied Mechanics and Engineering. 345: 1077-1093. DOI: 10.1016/J.Cma.2018.09.004  0.453
2019 Charnyi S, Heister T, Olshanskii MA, Rebholz LG. Efficient discretizations for the EMAC formulation of the incompressible Navier–Stokes equations Applied Numerical Mathematics. 141: 220-233. DOI: 10.1016/J.Apnum.2018.11.013  0.461
2019 Mohebujjaman M, Rebholz LG, Iliescu T. Physically constrained data‐driven correction for reduced‐order modeling of fluid flows International Journal For Numerical Methods in Fluids. 89: 103-122. DOI: 10.1002/Fld.4684  0.821
2018 Xie X, Mohebujjaman M, Rebholz LG, Iliescu T. Data-Driven Filtered Reduced Order Modeling of Fluid Flows Siam Journal On Scientific Computing. 40. DOI: 10.1137/17M1145136  0.8
2018 Akbas M, Linke A, Rebholz LG, Schroeder PW. The analogue of grad-div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes Computer Methods in Applied Mechanics and Engineering. 341: 917-938. DOI: 10.1016/J.Cma.2018.07.019  0.515
2018 Akbas M, Rebholz LG, Zerfas C. Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations Calcolo. 55: 1-29. DOI: 10.1007/S10092-018-0246-7  0.433
2017 Bowers AL, Rebholz LG. The Reduced NS-α Model for Incompressible Flow: A Review of Recent Progress Fluids. 2: 38. DOI: 10.3390/Fluids2030038  0.759
2017 Mohebujjaman M, Rebholz LG. An Efficient Algorithm for Computation of MHD Flow Ensembles Computational Methods in Applied Mathematics. 17: 121-137. DOI: 10.1515/Cmam-2016-0033  0.774
2017 Rebholz LG, Xiao M. Improved Accuracy in Algebraic Splitting Methods for Navier--Stokes Equations Siam Journal On Scientific Computing. 39. DOI: 10.1137/16M1061424  0.421
2017 John V, Linke A, Merdon C, Neilan M, Rebholz LG. On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows Siam Review. 59: 492-544. DOI: 10.1137/15M1047696  0.495
2017 Mohebujjaman M, Rebholz LG, Xie X, Iliescu T. Energy balance and mass conservation in reduced order models of fluid flows Journal of Computational Physics. 346: 262-277. DOI: 10.1016/J.Jcp.2017.06.019  0.817
2017 Charnyi S, Heister T, Olshanskii MA, Rebholz LG. On conservation laws of Navier–Stokes Galerkin discretizations Journal of Computational Physics. 337: 289-308. DOI: 10.1016/J.Jcp.2017.02.039  0.471
2017 Eroglu FG, Kaya S, Rebholz LG. A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows Computer Methods in Applied Mechanics and Engineering. 325: 350-368. DOI: 10.1016/J.Cma.2017.07.017  0.61
2017 Akbas M, Mohebujjaman M, Rebholz LG, Xiao M. High order algebraic splitting for magnetohydrodynamics simulation Journal of Computational and Applied Mathematics. 321: 128-142. DOI: 10.1016/J.Cam.2017.02.021  0.811
2017 Rebholz LG, Kim T, Byon Y. On an accurate α model for coarse mesh turbulent channel flow simulation Applied Mathematical Modelling. 43: 139-154. DOI: 10.1016/J.Apm.2016.10.059  0.486
2017 Heister T, Mohebujjaman M, Rebholz LG. Decoupled, Unconditionally Stable, Higher Order Discretizations for MHD Flow Simulation Journal of Scientific Computing. 71: 21-43. DOI: 10.1007/S10915-016-0288-4  0.79
2017 Rebholz L, Zerfas C, Zhao K. Global in Time Analysis and Sensitivity Analysis for the Reduced NS-α Model of Incompressible Flow Journal of Mathematical Fluid Mechanics. 19: 445-467. DOI: 10.1007/S00021-016-0290-5  0.524
2016 Berselli LC, Kim TY, Rebholz LG. Analysis of a reduced-order approximate deconvolution model and its interpretation as a navier-stokes-voigt regularization Discrete and Continuous Dynamical Systems - Series B. 21: 1027-1050. DOI: 10.3934/Dcdsb.2016.21.1027  0.48
2016 Neda M, Pahlevani F, Rebholz LG, Waters J. Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow Journal of Numerical Mathematics. 24: 189-206. DOI: 10.1515/Jnma-2015-1017  0.765
2016 Heister T, Rebholz LG, Xiao M. Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems Journal of Mathematical Analysis and Applications. 438: 507-513. DOI: 10.1016/J.Jmaa.2016.01.075  0.454
2016 Jiang N, Mohebujjaman M, Rebholz LG, Trenchea C. An optimally accurate discrete regularization for second order timestepping methods for Navier–Stokes equations Computer Methods in Applied Mechanics and Engineering. 310: 388-405. DOI: 10.1016/J.Cma.2016.07.017  0.816
2016 Cao Y, Chen S, Rebholz LG. Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow Computers and Mathematics With Applications. DOI: 10.1016/J.Camwa.2015.12.012  0.539
2016 Heister T, Olshanskii MA, Rebholz LG. Unconditional long-time stability of a velocity–vorticity method for the 2D Navier–Stokes equations Numerische Mathematik. 1-25. DOI: 10.1007/S00211-016-0794-1  0.446
2016 Akbas M, Kaya S, Rebholz LG. On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems Numerical Methods For Partial Differential Equations. DOI: 10.1002/Num.22061  0.632
2016 Morales Hernandez M, Rebholz LG, Tone C, Tone F. Stability of the Crank-Nicolson-Adams-Bashforth scheme for the 2D Leray-alpha model Numerical Methods For Partial Differential Equations. 32: 1155-1183. DOI: 10.1002/Num.22045  0.44
2016 Akbas M, Kaya S, Mohebujjaman M, Rebholz LG. Numerical analysis and testing of a fully discrete, decoupled penalty-projection algorithm for mhd in elsässer variable International Journal of Numerical Analysis and Modeling. 13: 90-113.  0.788
2015 Belenli MA, Kaya S, Rebholz LG. An explicitly decoupled variational multiscale method for incompressible, non-isothermal flows Computational Methods in Applied Mathematics. 15: 1-20. DOI: 10.1515/Cmam-2014-0026  0.638
2015 Cuff VM, Dunca AA, Manica CC, Rebholz LG. The reduced order NS- α model for incompressible flow: Theory, numerical analysis and benchmark testing Esaim: Mathematical Modelling and Numerical Analysis. 49: 641-662. DOI: 10.1051/M2An/2014053  0.816
2015 Morales Hernandez M, Rebholz LG. A note on helicity conservation in Leray models of incompressible flow Journal of Mathematical Analysis and Applications. 422: 776-781. DOI: 10.1016/J.Jmaa.2014.09.014  0.49
2015 Olshanskii MA, Heister T, Rebholz LG, Galvin KJ. Natural vorticity boundary conditions on solid walls Computer Methods in Applied Mechanics and Engineering. 297: 18-37. DOI: 10.1016/J.Cma.2015.08.011  0.369
2015 Rebholz LG, Xiao M. On reducing the splitting error in Yosida methods for the Navier-Stokes equations with grad-div stabilization Computer Methods in Applied Mechanics and Engineering. 294: 259-277. DOI: 10.1016/J.Cma.2015.06.013  0.49
2015 Le Borne S, Rebholz LG. Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems Computing and Visualization in Science. DOI: 10.1007/S00791-015-0236-0  0.425
2015 Monteiro IO, Manica CC, Rebholz LG. Numerical study of a regularized barotropic vorticity model of geophysical flow Numerical Methods For Partial Differential Equations. 31: 1492-1514. DOI: 10.1002/Num.21956  0.815
2015 Kim TY, Dunca AA, Rebholz LG, Fried E. Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows Mathematical Methods in the Applied Sciences. 38: 4199-4209. DOI: 10.1002/Mma.3358  0.83
2014 Galvin KJ, Rebholz LG, Trenchea C. Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models Siam Journal On Numerical Analysis. 52: 678-707. DOI: 10.1137/120887412  0.479
2014 Bowers AL, Le Borne S, Rebholz LG. Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization Computer Methods in Applied Mechanics and Engineering. 275: 1-19. DOI: 10.1016/J.Cma.2014.02.021  0.741
2014 Belenli MA, Rebholz LG, Tone F. A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements Applied Mathematics Letters. DOI: 10.1016/J.Aml.2015.01.018  0.442
2014 Kaya S, Manica CC, Rebholz LG. On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions Applied Mathematics and Computation. 246: 23-38. DOI: 10.1016/J.Amc.2014.07.102  0.839
2014 Jenkins E, John V, Linke A, Rebholz LG. On the parameter choice in grad-div stabilization for the stokes equations Advances in Computational Mathematics. 40: 491-516. DOI: 10.1007/S10444-013-9316-1  0.383
2013 Layton WJ, Rebholz LG. On relaxation times in the Navier-Stokes-Voigt model International Journal of Computational Fluid Dynamics. 27: 184-187. DOI: 10.1080/10618562.2013.766328  0.664
2013 Belenli MA, Kaya S, Rebholz LG, Wilson NE. A subgrid stabilization finite element method for incompressible magnetohydrodynamics International Journal of Computer Mathematics. DOI: 10.1080/00207160.2012.758363  0.664
2013 Rebholz LG. Well-posedness of a reduced order approximate deconvolution turbulence model Journal of Mathematical Analysis and Applications. 405: 738-741. DOI: 10.1016/J.Jmaa.2013.04.036  0.454
2013 Linke A, Rebholz LG. On a reduced sparsity stabilization of grad-div type for incompressible flow problems Computer Methods in Applied Mechanics and Engineering. 261: 142-153. DOI: 10.1016/J.Cma.2013.04.005  0.414
2013 Bowers AL, Rebholz LG. Numerical study of a regularization model for incompressible flow with deconvolution-based adaptive nonlinear filtering Computer Methods in Applied Mechanics and Engineering. 258: 1-12. DOI: 10.1016/J.Cma.2013.02.003  0.789
2013 Dunca AA, Neda M, Rebholz LG. A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity Computers and Mathematics With Applications. 66: 917-933. DOI: 10.1016/J.Camwa.2013.06.013  0.817
2013 Bowers AL, Kim TY, Neda M, Rebholz LG, Fried E. The Leray-αβ-deconvolution model: Energy analysis and numerical algorithms Applied Mathematical Modelling. 37: 1225-1241. DOI: 10.1016/J.Apm.2012.03.040  0.792
2013 Cousins BR, Borne SL, Linke A, Rebholz LG, Wang Z. Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements Numerical Methods For Partial Differential Equations. 29: 1217-1237. DOI: 10.1002/Num.21752  0.463
2012 Galvin KJ, Lee H, Rebholz LG. Approximation of viscoelastic flows with defective boundary conditions Journal of Non-Newtonian Fluid Mechanics. 169: 104-113. DOI: 10.1016/J.Jnnfm.2011.12.002  0.41
2012 Kim TY, Rebholz LG, Fried E. A deconvolution enhancement of the Navier-Stokes-αβ model Journal of Computational Physics. 231: 4015-4027. DOI: 10.1016/J.Jcp.2011.12.003  0.511
2012 Benzi M, Olshanskii MA, Rebholz LG, Wang Z. Assessment of a vorticity based solver for the Navier-Stokes equations Computer Methods in Applied Mechanics and Engineering. 247: 216-225. DOI: 10.1016/J.Cma.2012.07.016  0.509
2012 Galvin KJ, Linke A, Rebholz LG, Wilson NE. Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection Computer Methods in Applied Mechanics and Engineering. 237: 166-176. DOI: 10.1016/J.Cma.2012.05.008  0.455
2012 Kuberry P, Larios A, Rebholz LG, Wilson NE. Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows Computers and Mathematics With Applications. 64: 2647-2662. DOI: 10.1016/J.Camwa.2012.07.010  0.521
2012 Layton W, Rebholz LG, Trenchea C. Modular nonlinear filter stabilization of methods for higher reynolds numbers flow Journal of Mathematical Fluid Mechanics. 14: 325-354. DOI: 10.1007/S00021-011-0072-Z  0.662
2012 Layton WJ, Rebholz LG. Approximate deconvolution models of turbulence: Analysis, phenomenology and numerical analysis Lecture Notes in Mathematics. 2042: 1-192. DOI: 10.1007/978-3-642-24409-4_1  0.622
2012 Bowers AL, Rebholz LG. Increasing accuracy and efficiency in FE computations of the Leray-Deconvolution model Numerical Methods For Partial Differential Equations. 28: 720-736. DOI: 10.1002/Num.20653  0.789
2012 Dunca AA, Kohler KE, Neda M, Rebholz LG. A mathematical and physical Study of multiscale deconvolution models of turbulence Mathematical Methods in the Applied Sciences. 35: 1205-1219. DOI: 10.1002/Mma.2514  0.8
2012 Bowers AL, Rebholz LG, Takhirov A, Trenchea C. Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering International Journal For Numerical Methods in Fluids. 70: 805-828. DOI: 10.1002/Fld.2732  0.803
2011 Manica CC, Neda M, Olshanskii M, Rebholz LG, Wilson NE. On an Efficient Finite Element Method for Navier-Stokes-w̄ with Strong Mass Conservationv Computational Methods in Applied Mathematics. 11: 3-22. DOI: 10.2478/Cmam-2011-0001  0.816
2011 Lee HK, Olshanskii MA, Rebholz LG. On error analysis for the 3d navier-stokes equations in velocity-vorticity-helicity form Siam Journal On Numerical Analysis. 49: 711-732. DOI: 10.1137/10080124X  0.507
2011 Case MA, Ervin VJ, Linke A, Rebholz LG. A connection between Scott-Vogelius and grad-div stabilized Taylor-Hood fe approximations of the Navier-Stokes equations Siam Journal On Numerical Analysis. 49: 1461-1481. DOI: 10.1137/100794250  0.472
2011 Connors JM, Jenkins EW, Rebholz LG. Small-scale divergence penalization for incompressible flow problems via time relaxation International Journal of Computer Mathematics. 88: 3202-3216. DOI: 10.1080/00207160.2011.581752  0.619
2011 Manica CC, Neda M, Olshanskii M, Rebholz LG. Enabling numerical accuracy of Navier-Stokes- α through deconvolution and enhanced stability Esaim: Mathematical Modelling and Numerical Analysis. 45: 277-307. DOI: 10.1051/M2An/2010042  0.816
2011 Linke A, Rebholz LG, Wilson NE. On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems Journal of Mathematical Analysis and Applications. 381: 612-626. DOI: 10.1016/J.Jmaa.2011.03.019  0.408
2011 Kim TY, Neda M, Rebholz LG, Fried E. A numerical study of the Navier-Stokes-αβ model Computer Methods in Applied Mechanics and Engineering. 200: 2891-2902. DOI: 10.1016/J.Cma.2011.05.011  0.467
2011 Cousins BR, Rebholz LG, Wilson NE. Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations Applied Mathematics and Computation. 218: 1208-1221. DOI: 10.1016/J.Amc.2011.05.111  0.497
2010 Rebholz LG, Sussman MM. On the high accuracy ns-alpha-deconvolution turbulence model Mathematical Models and Methods in Applied Sciences. 20: 611-633. DOI: 10.1142/S0218202510004362  0.423
2010 Layton W, Rebholz L, Sussman M. Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models Ima Journal of Applied Mathematics. 75: 56-74. DOI: 10.1093/Imamat/Hxp034  0.565
2010 Bowers AL, Cousins BR, Linke A, Rebholz LG. New connections between finite element formulations of the Navier-Stokes equations Journal of Computational Physics. 229: 9020-9025. DOI: 10.1016/J.Jcp.2010.08.036  0.754
2010 Olshanskii MA, Rebholz LG. Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations Journal of Computational Physics. 229: 4291-4303. DOI: 10.1016/J.Jcp.2010.02.012  0.414
2010 Olshanskii M, Rebholz LG. Note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations Computer Methods in Applied Mechanics and Engineering. 199: 1032-1035. DOI: 10.1016/J.Cma.2009.11.015  0.343
2010 Layton W, Manica CC, Neda M, Rebholz LG. Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations Computer Methods in Applied Mechanics and Engineering. 199: 916-931. DOI: 10.1016/J.Cma.2009.01.011  0.8
2010 Layton WJ, David Pruett C, Rebholz LG. Temporally regularized direct numerical simulation Applied Mathematics and Computation. 216: 3728-3738. DOI: 10.1016/J.Amc.2010.05.031  0.684
2010 Miles WW, Rebholz LG. An enhanced-physics-based scheme for the NS-α turbulence model Numerical Methods For Partial Differential Equations. 26: 1530-1555. DOI: 10.1002/Num.20509  0.449
2009 Rebholz LG. Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models Advances in Numerical Analysis. 2009: 1-13. DOI: 10.1155/2009/370289  0.464
2009 Layton W, Manica CC, Neda M, Olshanskii M, Rebholz LG. On the accuracy of the rotation form in simulations of the Navier-Stokes equations Journal of Computational Physics. 228: 3433-3447. DOI: 10.1016/J.Jcp.2009.01.027  0.799
2009 Labovsky A, Layton WJ, Manica CC, Neda M, Rebholz LG. The stabilized extrapolated trapezoidal finite-element method for the Navier-Stokes equations Computer Methods in Applied Mechanics and Engineering. 198: 958-974. DOI: 10.1016/J.Cma.2008.11.004  0.814
2008 Rebholz LG. A family of new, high order NS-α models arising from helicity correction in Leray turbulence models Journal of Mathematical Analysis and Applications. 342: 246-254. DOI: 10.1016/J.Jmaa.2007.11.031  0.438
2008 Rebholz LG, Layton W, Manica CC, Neda M. Numerical analysis and computational testing of a high accuracy leray-deconvolution model of turbulence Numerical Methods For Partial Differential Equations. 24: 555-582. DOI: 10.1002/Num.20281  0.829
2008 Layton WJ, Manica CC, Neda M, Rebholz LG. Helicity and energy conservation and dissipation in approximate deconvolution les models of turbulence Advances and Applications in Fluid Mechanics. 4: 1-46.  0.803
2007 Rebholz LG. An energy- and helicity-conserving finite element scheme for the Navier-Stokes equations Siam Journal On Numerical Analysis. 45: 1622-1638. DOI: 10.1137/060651227  0.453
2007 Rebholz LG. Conservation laws of turbulence models Journal of Mathematical Analysis and Applications. 326: 33-45. DOI: 10.1016/J.Jmaa.2006.02.026  0.476
2006 Rebholz LG. A multiscale V-P discretization for flow problems Applied Mathematics and Computation. 177: 24-35. DOI: 10.1016/J.Amc.2005.10.030  0.451
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