Preprints

• Inverse problems for Physics-Based Process Models, Troy Butler, Derek Bingham, Don Estep, Annual Reviews, 2020, under review

 

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. 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.

13. 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

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

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

16. 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).

17. 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.

18. 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.

19. 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.

20. 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

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

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. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

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

46. 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

47. 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

48. 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)

49. 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

50. 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

51. 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

52. 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

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

54. 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

55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

61. 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

62. 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

63. 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

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

65. 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

66. 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

67. 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

68. 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

69. A stochastic inverse problem for multiscale models, N. Panda, T. Butler, D. Estep, L. Graham, and C. Dawson, Journal for Multiscale Computational Engineering, 15 (2017), 265-283

70. Efficient distribution estimation and uncertainty quantification for elliptic problems on domains with stochastic boundaries, J. H. Chaudhry, N. Burch, D. Estep, SIAM/ASA Journal on Uncertainty Quantification 6 (2018), 1127-1150

71. Adjoint methods for uncertainty quantification in applied computational electromagnetics: FEM scattering examples, C. Key, A. Smull, B. M. Notaros, D. Estep, and T. Butler, Invited Paper, Special Issue Advanced Computational Electromagnetic Methodologies and Techniques, ACES Journal, February 2019, ISBN: 978-0-9960078-8-7

72. A posteriori error estimation and adaptive discretization refinement using adjoint methods in CEM: A study with a one-dimensional higher-order FEM scattering example, C. Key, A. Smull, D. Estep, T. Butler, and B. M. Notaros, IEEE Transactions on Antennas and Propagation, 68 (2020), 3791-3806

73. Adjoint-based accelerated adaptive refinement in frequency domain 3-D finite element method scattering problems, J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaros, IEEE Transactions on Antennas and Propagation, (2020), 69 (2020), 940-949

74. Error estimation and uncertainty quantification for first time to a threshold value, J. H. Chaudhry, D. Estep, Z. Stevens, and S. Tavener, BIT Numerical Mathematics, (2020), https://doi.org/10.1007/s10543-020-00825-0

75. A posteriori error analysis for Schwarz overlapping domain decomposition methods, J. H. Chaudhry, D. Estep, S. Tavener, BIT Numerical Mathematics, 2021, 0.1007/s10543-021-00864-1

76. Adjoint sensitivity analysis for uncertain material parameters in frequency-domain 3-D FEM, J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaros, IEEE Transactions on Antennas and Propagation, 69 (2021), 6669-6679

77. Learning quantities of interest from dynamical systems for data-consistent inversion, S. Mattis, K.R. Steffen, T. Butler, C.N. Dawson, and D. Estep, Computer Methods in Applied Mechanics and Engineering, 2021, accepted

 

Peer-Reviewed Conference Papers

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. Adjoint methods for uncertainty quantification in applied computational electromagnetics: FEM scattering examples, C. Key, A. Smull, B. M. Notaros, D. Estep, and T. Butler, Proceedings of the 2018 International Applied Computational Electromagnetics Society (ACES) Symposium – ACES2018, March 25–29, 2018, Denver, Colorado, USA

8. A posteriori element-wise error quantification for FEM solvers using higher order basis functions, C. Key, A. Smull, D. Estep, T. Butler, and B. M. Notaros, Proceedings of the 2018 IEEE International Symposium on Antennas and Propagation, July 8–13, 2018, Boston, MA, USA, pp. 1319–1320

9. Applications of adjoint solutions for predicting and analyzing numerical error of forward solutions based on higher order finite element modeling, B. M. Notaros, C. Key, A. Smull, D. Estep, and T. Butler, Proceedings of the 14th International Workshop on Finite Elements for Microwave Engineering – FEM2018, September 10-14, 2018, Cartagena de Indias, Colombia, pp. 3–4

10. Adjoint-based a posteriori error estimation and its applications in CEM: DHO FEM techniques and 3D scattering problems, J. Harmon, C. Key, B. Troksa, T. Butler, D. Estep, and B. M. Notaros, Proc. 2019 USNC-URSI National Radio Science Meeting, January 9-12, 2019, Boulder, Colorado

11. Adjoint-based uncertainty quantification in frequency-domain double higher-order FEM, J. Harmon, C. Key, B. M. Notaros, D. Estep, and T. Butler, Proceedings of the 2019 International Applied Computational Electromagnetics Society (ACES) Symposium – ACES2019, April 15–19, 2019, Miami, Florida, USA

12. Overview of some advances in higher order frequency-domain CEM techniques, B. M. Notaros, S. B. Manic, C. Key, J. Harmon, and D. Estep, Invited Paper, Special Session Advances in Frequency-Domain CEM Techniques and Applications, accepted for the 21st International Conference on Electromagnetics in Advanced Applications – ICEAA 2019, September 9-13, 2019, Granada, Spain

13. Error estimation and uncertainty quantification based on adjoint methods in computational electromagnetics, B. M. Notaros, J. Harmon, C. Key, D. Estep, and T. Butler, Invited Paper, Special Session Applications of Machine/Deep Learning and Uncertainty Quantification Techniques in Computational Electromagnetics, accepted for 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting – AP-S/URSI 2019, July 7–12, 2019, Atlanta, GA

 

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

3. 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.

4. Interview, SIAM News 43 (2010)