Donald Estep

Papers

Research Articles

1. Boundedness of dispersive difference schemes, D. Estep, M. Loss, and J. Rauch, Mathematics of Computation 55 (1990), 55-87

2. Some stability aspects of schemes for the adaptive integration of stiff initial value problems, L. Dieci and D. Estep, SIAM Journal on Scientific and Statistical Computing 12 (1991), 1284-1303

3. The discontinuous Galerkin method for semilinear parabolic problems, D. Estep and S. Larsson, RAIRO Modélisation Mathématique et Analyse Numérique 27 (1993), 35-54

4. Global error control for the continuous Galerkin finite element method for ordinary differential equations, D. Estep and D. French, RAIRO Modélisation Mathématique et Analyse Numérique 28 (1994), 815-852

5. An analysis of numerical approximations of metastable solutions of the bistable equation, D. Estep, Nonlinearity 7 (1994), 1445-1462

6. A normal form analysis of dispersion in numerical schemes for the linear Korteweg-deVries equation, D. Estep, Applicable Analysis 52 (1994), 53-68

7. A posteriori error bounds and global error control for approximations of ordinary differential equations, D. Estep, SIAM Journal on Numerical Analysis 32 (1995), 1-48

8. Error growth in Hamiltonian-conserving integrators, D. Estep and A. Stuart, Zeitschrift für Angewandte Mathematik und Physik 46 (1995), 407-418

9. Introduction to adaptive methods for differential equations, K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Acta Numerica (1995), 105-158.

10. h-adaptive boundary element schemes, C. Carstensen, D. Estep and E. Stephan, Computational Mechanics 15 (1995), 372-383.

11. A modified equation for dispersive difference schemes, D. Estep, Applied Numerical Mathematics 17 (1995), 299-309

12. Accurate parallel integration of large sparse systems of differential equations, D. Estep

and R. Williams, Mathematical Models and Methods in Applied Sciences 6 (1996), 535-568

13. Adaptive methods for reaction diffusion problems, D. Estep, M. Larson and R. Williams, Proceedings of the 12'th Annual Review of Progress in Applied Computational Electromagnetics, 1996, 611-618

14. The computability of the Lorenz system, D. Estep and C. Johnson, Mathematical Models and Methods in Applied Sciences 8 (1998), 1277-1305

15. Computational error estimation and adaptive mesh refinement for a finite element solution of launch vehicle trajectory problems, D. Estep, D. Hodges and M. Warner, SIAM Journal on Scientific Computing 21 (2000), 1609-1631 (electronic).

16. Using Krylov-subspace iterations in discontinuous Galerkin methods for nonlinear reaction-diffusion systems, D. Estep and R. Freund, in Lecture Notes in Computational Science and Engineering 11, B. Cockburn, G. E. Karniadakis, C. -W. Shu, Eds, Springer-Verlag, New York, 2000, 327-336.

17. The solution of a launch vehicle trajectory problem by an adaptive finite element method, D. Estep, D. H. Hodges, M. Warner, Computer Methods in Applied Mechanics and Engineering, 190 (2001), 4677-4690.

18. Analysis of shear layers in a fluid with temperature-dependent viscosity, D. Estep, S. Verduyn Lunel, and R. Williams, Journal on Computational Physics 173 (2001), 17-60.

19. Accounting for stability: a posteriori estimates based on residuals and variational analysis, D. Estep, M. Holst, D. Mikulencak, Communications in Numerical Methods in Engineering 18 (2002), 15-30

20. The dynamical behavior of the discontinuous Galerkin method and related difference schemes, D. Estep and A. Stuart, Mathematics of Computation 71 (2002), 1075-1103

21. The formation of shear layers in a fluid with temperature-dependent viscosity, D. Estep, S. Verduyn Lunel, and R. Williams, Equadiff 03, International Conference on Differential Equations, Hasselt 2003, World Scientific, Singapore, 2004

22. Generalized Green’s functions and the effective domain of influence, D. Estep, M. Holst, and M. Larson, SIAM Journal on Scientific Computing 26 (2005), 1314-1339

23. Fast and reliable methods for determining the evolution of uncertain parameters in differential equations, D. Estep and D. Neckels, Journal on Computational Physics 213 (2006), 530-556

24. The nonlinear power method, S. Eastman and D. Estep, Applicable Analysis 86 (2007), 1303 – 1314

25. Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations, D. Estep and D. Neckels, Computer Methods in Applied Mechanics and Engineering 196 (2007), 3967 – 3979

26. Introducing FACETS, the Framework Application for Core-Edge Transport Simulations, J. R. Cary, J. Candy, R. H. Cohen, S. Krasheninnikov, D. C. McCune, D. J. Estep, J. Larson, A. D. Malony, P. H. Worley, J. A. Carlsson, A. H. Hakim, P. Hamill, S. Kruger, S. Muzsala, A. Pletzer, S. Shasharina, D. Wade-Stein, N. Wang, L. McInnes, T. Wildey, T. Casper, L. Diachin, T. Epperly, T. D. Rognlien, M. R. Fahey, J. A. Kuehn, A. Morris, S. Shende, E. Feibush, G. W. Hammett, K. Indireshkumar, C. Ludescher, L. Randerson, D. Stotler, A. Yu Pigarov, .P Bonoli, C. S. Chang, D. A. D’Ippolito, P. Colella, D. E. Keyes, R. Bramley, J. R. Myra, Journal of Physics: Conference Series 78 (2007), 1-6

27. A posteriori – a priori analysis of multiscale operator splitting, D. Estep, V. Ginting, D. Ropp, J. Shadid, and S. Tavener, SIAM Journal on Numerical Analysis 46 (2008), 1116-1146

28. Continuum modeling of large networks, E. Chong, D. Estep, and J. Hannig, International Journal of Numerical Modeling: Electronic Networks, Devices, and Fields, 21 (2008), 169-186

29. A posteriori error estimation of approximate boundary fluxes, T. Wildey, S. Tavener, and D. Estep, Communications in Numerical Methods in Engineering,  24 (2008), 421-434

30. A posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem, D. Estep, S. Tavener, T. Wildey, SIAM Journal on Numerical Analysis, 46 (2008), 2068-2089

31. Analysis of the sensitivity properties of a model of vector-borne bubonic plague, M. Buzby, D. Neckels, M. Antolin, and D. Estep, Royal Society Journal Interface, 5 (2008), 1099-1107

32. First results from core-edge parallel composition in the FACETS project, J. R. Cary, J. Candy, R. H. Cohen, S. Krasheninnikov, D. C. McCune, D. J. Estep, J. Larson, A. D. Malony, P. H. Worley, J. A. Carlsson, A. H. Hakim, P. Hamill, S. Kruger, M. Mia, S. Muzsala, A. Pletzer, S. Shasharina, D. Wade-Stein, N. Wang, S. Balay, L. McInnes, H. Zhang, T. Casper, L. Diachin, T. Epperly, T. D. Rognlien, M. R. Fahey, J. Cobb, A. Morris, S. Shende, G. W. Hammett, K. Indireshkumar, D. Stotler, A. Yu Pigarovd, Journal of Physics: Conference Series 125 (2008), 1-5

33. A posteriori error analysis of multiscale operator decomposition methods for multiphysics models, D. Estep, V. Carey, V. Ginting, S. Tavener, T. Wildey, Journal of Physics: Conference Series 125 (2008), 1-16

34. A posteriori analysis and adaptive error control for multiscale operator decomposition methods for coupled elliptic systems I: One way coupled systems, V. Carey, D. Estep, and S. Tavener, SIAM Journal on Numerical Analysis 47 (2009), 740-761

35. Nonparametric density estimation for randomly perturbed  elliptic problems II:   Applications and adaptive modeling, D. Estep, A. Malqvist, S. Tavener, International Journal for Numerical Methods in Engineering 80 (2009), 846-867

36. A posteriori error analysis for a transient conjugate heat transfer problem, D. Estep, S. Tavener, T. Wildey, Finite Elements in Analysis and Design 45 (2009), 263-271

37. Nonparametric density estimation for randomly perturbed  elliptic problems I:   Computational methods, a posteriori analysis, and adaptive error control, D. Estep, A. Malqvist, and S. Tavener, SIAM Journal on Scientific Computing 31 (2009), 2935-2959

38. A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems, D. Estep, M. Pernice, D. Pham, S. Tavener, H. Wang, Journal of Computational and Applied Mathematics 233 (2009), 459-472

39. A posteriori error estimation and adaptive mesh refinement for a multi-discretization operator decomposition approach to fluid-solid heat transfer, D. Estep, S. Tavener, T. Wildey, Journal of Computational Physics 229 (2010), 4143-4158

40. Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions, V. Carey, D. Estep, A. Johansson, M. Larson, and S. Tavener, SIAM Journal on Scientific Computing 32 (2010), 2121-2145

41. A measure-theoretic computational  method for inverse sensitivity problems I: Method and analysis, J. Breidt, T. Butler and D. Estep, SIAM Journal on Numerical Analysis 49 (2011), 1836-1859

42. A posteriori error analysis for a cut cell finite volume method, D. Estep, S. Tavener, M. Pernice and H. Wang, Computer Methods in Applied Mechanics and Engineering 200 (2011), 2768-2781

43. Nonparametric density estimation for randomly perturbed elliptic problems III: Convergence, complexity, and generalizations, D. Estep, M. Holst, A. Malqvist, Journal of Applied Mathematics and Computing 38 (2012), 367-387

44. Parameter estimation and directional leverage with applications in differential equations, N. Burch, D. Estep, and J. Hoeting, Metrika, DOI: 10.1007/s00184-011-0358-4, 2011

45. Continuum modeling and control of large mobile networks, Y. Zhang, E. K. P. Chong, J. Hannig, and D. Estep, Proceedings of the 49th Annual Allerton Conference on Communication, Control and Computing, Illinois, 2011, 1670-1677

46. A computational measure theoretic approach to inverse sensitivity problems II: A posteriori error analysis, T. Butler, D. Estep and J. Sandelin, SIAM Journal on Numerical Analysis, 50 (2012), 22-45

47. Viscoelastic effects during loading play an integral role in soft tissue mechanics, K. Troyer, D. Estep, and C. Puttlitz, Acta Biomaterialia 8 (2012), 234-244

48. A posteriori analysis of multirate numerical method for ordinary  differential equations, D. Estep, V. Ginting, S. Tavener, 2012, Computer Methods in Applied Mechanics and Engineering, 223-224 (2012), 10-27

49. Adaptive error control for an elliptic optimization problem, Applicable Analysis, D. Estep and S. Lee, 2012, DOI:10.1080/00036811.2012.683785, 1-15

50. Analysis of routing protocols and interference-limited communication in large networks via continuum modeling, N. Burch, E. Chong, D. Estep, J. Hannig, Journal of Engineering Mathematics, 79 (2013), 183-199

51. A numerical method for solving a stochastic inverse problem for parameters, T. Butler and D. Estep, Annals of Nuclear Energy, 2012, 86-94, 10.1016/j.anucene.2012.05.016

52. Multiphysics Simulations: Challenges and Opportunities, D. E. Keyes, L. C. McInnes, C. Woodward, W. Gropp, E. Myra, M. Pernice, J. Bell, J. Brown, A. Clo, J. Connors, E. Constantinescu, D. Estep, K. Evans, C. Farhat, A. Hakim, G. Hammond, G. Hansen, J. Hill, T. Isaac, X. Jiao, K. Jordan, D. Kaushik, E. Kaxiras, A. Koniges, K. Lee, A. Lott, Q. Lu, J. Magerlein, R. Maxwell, M. McCourt, M. Mehl, R. Pawlowski, A. Peters Randles, D. Reynolds, B. Riviere, U. Ruede, T. Scheibe, J. Shadid, B. Sheehan, M. Shephard, A. Siegel, B. Smith, X. Tang, C. Wilson, and B. Wohlmuth, International Journal of High Performance Computing Applications 27 (2013)

53. Continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations, Y. Zhang, E. Chong, J. Hannig, and D. Estep, Abstract and Applied Analysis 16 (2013), doi:10.1155/2013/262581, 1-16

54. A posteriori analysis of an iterative multi-discretization method for reaction-diffusion systems, D. Estep. V. Ginting, J. Hameed, and S. Tavener, Computer Methods in Applied Mechanics and Engineering, 267 (2013), 1-22

55. A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems, V. Carey, D. Estep, S. Tavener, International Journal of Numerical Methods in Engineering 94 (2013), 826-849

56. A-posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with non-matching grids, T. Arbogast, D. Estep, B. Sheehan, and S. Tavener, IMA J. Numerical Analysis, 2013, doi: 10.1093/imanum/drt049

57. Approximating extremely large networks via continuum limits, Y. Zhang, E. Chong, J. Hannig, and D. Estep, IEEE Access, 1 (2013), 577-595

58. A posteriori error estimation for the Lax-Wendroff finite difference scheme, J. B. Collins, D. Estep, and S. Tavener, Journal of Computational and Applied Mathematics 263C (2014), 299-311

59. A measure-theoretic computational  method for inverse sensitivity problems III:  Multiple quantities of interest, T. Butler, D. Estep, S. Tavener, C. Dawson, J. Westerink, SIAM ASA Journal on Uncertainty Quantification, 2 (2014), 174-202

60. A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques, J. Collins, D. Estep and S. Tavener, BIT Numerical Mathematics, December 2014, DOI 10.1007/s10543-014-0534-9

61. Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs, D. Elfverson, D. Estep, F. Hellman, A. Malqvist, SIAM ASA Journal on Uncertainty Quantification, 2 (2014), 826–850

62. A posteriori error analysis of IMEX time integration schemes for advection-diffusion-reaction equations, J. Chaudry, D. Estep, V. Ginting, J. Shadid, and S. Tavener, Computer Methods in Applied Mechanics and Engineering, 285 (2014), 730-751

63. The interaction of iteration error and stability for linear partial differential equations coupled through an interface, B. Sheehan, D. Estep, S. Tavener, J. Cary, S. Kruger, A. Hakim, A. Pletzer, J. Carlsson, and S. Vadlamani, Advances in Mathematical Physics, 2015, 13 pages, doi:10.1155/2015/787198

64. A posteriori error estimates for mixed finite element and finite volume methods for parabolic problems coupled through a boundary with non-matching discretizations, T. Arbogast, D. Estep, B. Sheehan, and S. Tavener, SIAM ASA Journal on Uncertainty Quantification, 3 (2015), 169-198

65. Adaptive finite element solution of multiscale PDE-ODE systems, A. Johansson, J. H. Chaudhry, V. Carey, D. Estep, V. Ginting, M. Larson, and S. Tavener, CMAME, 287 (2015), 150–171

66. Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models, T. Butler, L. Graham, D. Estep, C. Dawson, and J.J. Westerink, Advances in Water Resources, 78 (2015), 60–79

67. A posteriori analysis for iterative solvers for non-autonomous evolution problems, J. H. Chaudry, D. Estep, V. Ginting, and S. Tavener, SIAM ASA Journal on Uncertainty Quantification, 3 (2015), http://dx.doi.org/10.1137/130949403

68. On a perturbation method for stochastic parabolic PDE, D. Estep and P. Polyakov, Communications in Mathematics and Statistics: 3 (2015), 215-226

69. A posteriori error estimation for a cut cell finite volume method with uncertain interface location, J. B. Collins, D. Estep, and S. Tavener, International Journal of Uncertainty Quantification, 5 (2015), 415-432

70. Parameter estimation and prediction for groundwater contamination based on measure theory, Troy Butler, Clint Dawson, Donald Estep, Steven Mattis, Velimir Vesselinov, Water Resources Research, 52 (2015), 7808-7629

71. A posteriori error analysis of two stage computation methods with application to efficient resource allocation and the Parareal Algorithm, J. H. Chaudhry, D. Estep, S. Tavener, V. Carey, and J . Sandelin, SIAM J. Numerical Analysis, 54 (2016), 2729-3122

72. Exploration of efficient reduced-order modeling and a posteriori error estimation, J. H. Chaudhry, D. Estep and M. Gunzburger, International Journal on Numerical Methods in Engineering, 111 (2016), 102-122

73. A stochastic inverse problem for multiscale models, N. Panda, T. Butler, D. Estep, L. Graham, and C. Dawson, Journal for Multiscale Computational Engineering, to appear.

 

Invited Articles

1. Error estimation for numerical differential equations, D. Estep, S. Verduyn Lunel and R. Williams, IEEE Antenna and Propagation Magazine 38 (1996), 71-76

 

Non-refereed Articles

1. Boundedness of dispersive difference schemes via a normal form analysis, D. Estep, Proceedings of the Third International Conference on Hyperbolic Problems, 1990

2. Introduction to computational methods for differential equations, K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, in Theory of Numerics for Ordinary and Partial Differential Equations, M. Ainsworth, J. Levesley, W. A. Light, and M. Marletta, eds, Oxford University Press, New York, 1995.

3. CSE 2009: Graduate Education in CSE - Structure for the Zoo? H.-J. Bungartz and D. Estep, in SIAM News 42, 2009.

4. Computational Science and Engineering Education: SIAM's Perspective, H.-J. Bungartz, D. Estep, U. Rude, and P. Turner, IEEE Computing in Science and Engineering 11 (2009), 5-11.

5. Interview, SIAM News 43 (2010)