Edit Profile (opens in new tab) Estep, Donald J. Co-Author Distance Author ID: estep.donald-j Published as: Estep, Donald; Estep, D.; Estep, Don; Estep, Donald J. more...less Homepage: https://www.stat.colostate.edu/~estep/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef Documents Indexed: 78 Publications since 1990, including 8 Books and 1 Additional arXiv Preprint 2 Contributions as Editor Co-Authors: 56 Co-Authors with 72 Joint Publications 1,918 Co-Co-Authors all top 5 Co-Authors 8 single-authored 31 Tavener, Simon J. 10 Chaudhry, Jehanzeb Hameed 8 Johnson, Claes G. L. 7 Eriksson, Kenneth 6 Ginting, Victor 5 Butler, Troy D. 5 Carey, Varis 4 Larson, Mats G. 4 Målqvist, Axel 4 Williams, Roy D. 3 Burch, Nathanial 3 Chong, Edwin Kah Pin 3 Collins, Joseph B. 3 Dawson, Clint N. 3 Hannig, Jan 3 Hansbo, Peter 3 Holst, Michael J. 2 Arbogast, Todd 2 Dieci, Luca 2 Hodges, Dewey H. 2 Johansson, August 2 Neckels, D. 2 Pernice, Michael 2 Sandelin, Jeff 2 Shadid, John N. 2 Stevens, Zachary 2 Stuart, Andrew M. 2 Verduyn Lunel, Sjoerd M. 2 Wang, Haiying 2 Warner, Michael S. 1 Breidt, J. 1 Carstensen, Carsten 1 Eastman, Sean 1 Elfverson, Daniel 1 French, Donald A. 1 Freund, Roland W. 1 Giannini, Trevor 1 Graham, Lindley 1 Hellman, Fredrik 1 Hoeting, Jennifer A. 1 Larsson, Stig 1 Lee, Sheldon 1 Loss, Michael 1 Mattis, Steven A. 1 Mikulencak, Duane R. 1 Pham, Du 1 Polyakov, Peter L. 1 Rauch, Jeffrey B. 1 Reid, Nancy 1 Ropp, David L. 1 Steffen, Kyle R. 1 Van de Velde, Eric F. 1 Westerink, Joannes J. 1 Wildey, Tim M. 1 Wildey, Timothy M. 1 Zhang, Yang all top 5 Serials 8 Computer Methods in Applied Mechanics and Engineering 7 SIAM Journal on Numerical Analysis 5 SIAM/ASA Journal on Uncertainty Quantification 4 BIT 4 SIAM Journal on Scientific Computing 3 Applicable Analysis 3 Journal of Computational Physics 2 Mathematics of Computation 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Communications in Numerical Methods in Engineering 1 The Canadian Journal of Statistics 1 IMA Journal of Numerical Analysis 1 Journal of Engineering Mathematics 1 Metrika 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Memoirs of the American Mathematical Society 1 SIAM Journal on Scientific and Statistical Computing 1 Applied Numerical Mathematics 1 Computational Mechanics 1 Numerical Methods for Partial Differential Equations 1 Numerical Algorithms 1 Abstract and Applied Analysis 1 International Journal of Numerical Modelling 1 Journal of Applied Mathematics and Computing 1 Advances in Mathematical Physics 1 International Journal for Uncertainty Quantification 1 Communications in Mathematics and Statistics 1 Undergraduate Texts in Mathematics 1 Springer-Lehrbuch all top 5 Fields 66 Numerical analysis (65-XX) 33 Partial differential equations (35-XX) 18 Ordinary differential equations (34-XX) 9 Probability theory and stochastic processes (60-XX) 9 Fluid mechanics (76-XX) 8 General and overarching topics; collections (00-XX) 4 Statistics (62-XX) 4 Mechanics of particles and systems (70-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Mathematics education (97-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Real functions (26-XX) 3 Measure and integration (28-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 1 Operator theory (47-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 65 Publications have been cited 946 times in 597 Documents Cited by ▼ Year ▼ Introduction to adaptive methods for differential equations. Zbl 0829.65122 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 217 1995 Computational differential equations. Zbl 0946.65049 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 95 1996 A posteriori error bounds and global error control for approximation of ordinary differential equations. Zbl 0820.65052 Estep, Donald 79 1995 Estimating the error of numerical solutions of systems of reaction-diffusion equations. Zbl 0998.65096 Estep, Donald J.; Larson, Mats G.; Williams, Roy D. 59 2000 Global error control for the continuous Galerkin finite element method for ordinary differential equations. Zbl 0822.65054 Estep, Donald; French, Donald 38 1994 Generalized Green’s functions and the effective domain of influence. Zbl 1078.65095 Estep, Donald; Holst, Michael; Larson, Mats 29 2005 An a posteriori-a priori analysis of multiscale operator splitting. Zbl 1166.65367 Estep, D.; Ginting, V.; Ropp, D.; Shadid, J. N.; Tavener, S. 20 2008 The discontinuous Galerkin method for semilinear parabolic problems. Zbl 0768.65065 Estep, Donald; Larsson, S. 19 1993 A posteriori analysis and adaptive error control for multiscale operator decomposition solution of elliptic systems. I: Triangular systems. Zbl 1186.65142 Carey, V.; Estep, D.; Tavener, S. 18 2009 Accounting for stability: A posteriori error estimates based on residuals and variational analysis. Zbl 0994.65097 Estep, Donald; Holst, Michael; Mikulencak, Duane 13 2002 A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques. Zbl 1332.65120 Collins, J. B.; Estep, D.; Tavener, S. 13 2015 Nonparametric density estimation for randomly perturbed elliptic problems. I: Computational methods, a posteriori analysis, and adaptive error control. Zbl 1194.65128 Estep, D.; Målqvist, A.; Tavener, S. 13 2009 A posteriori analysis of a multirate numerical method for ordinary differential equations. Zbl 1253.65118 Estep, Donald J.; Ginting, Victor; Tavener, Simon J. 13 2012 Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions. Zbl 1216.65127 Carey, V.; Estep, D.; Johansson, A.; Larson, M.; Tavener, S. 12 2010 A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer. Zbl 1281.80004 Estep, Donald; Tavener, Simon; Wildey, Tim 12 2010 A measure-theoretic computational method for inverse sensitivity problems. I: Method and analysis. Zbl 1234.60062 Breidt, J.; Butler, T.; Estep, D. 12 2011 The dynamical behavior of the discontinuous Galerkin method and related difference schemes. Zbl 0998.65080 Estep, Donald J.; Stuart, Andrew M. 12 2002 A posteriorierror analysis of a cell-centered finite volume method for semilinear elliptic problems. Zbl 1176.65125 Estep, Don; Pernice, Michael; Pham, Du; Tavener, Simon; Wang, Haiying 12 2009 A posteriori error analysis of two-stage computation methods with application to efficient discretization and the parareal algorithm. Zbl 1350.65074 Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff 12 2016 A posteriori error analysis of IMEX multi-step time integration methods for advection-diffusion-reaction equations. Zbl 1425.65086 Chaudhry, Jehanzeb H.; Estep, Donald; Ginting, Victor; Shadid, John N.; Tavener, Simon 12 2015 Error estimates for multiscale operator decomposition for multiphysics models. Zbl 1218.65100 Estep, D. 11 2010 A posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem. Zbl 1176.65124 Estep, D.; Tavener, S.; Wildey, T. 11 2008 A posteriori error estimation for the Lax-Wendroff finite difference scheme. Zbl 1302.65184 Collins, J. B.; Estep, Don; Tavener, Simon 11 2014 Practical analysis in one variable. Zbl 1038.26001 Estep, Donald 11 2002 A posteriori error estimates for mixed finite element and finite volume methods for parabolic problems coupled through a boundary. Zbl 1322.65093 Arbogast, T.; Estep, D.; Sheehan, B.; Tavener, S. 10 2015 A posteriori analysis of an iterative multi-discretization method for reaction-diffusion systems. Zbl 1286.65121 Chaudhry, J. H.; Estep, D.; Ginting, V.; Tavener, S. 10 2013 \(h\)-adaptive boundary element schemes. Zbl 0821.65072 Carstensen, C.; Estep, Donald; Stephan, P. 9 1995 Introduction to computational methods for differential equations. Zbl 0843.65057 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 9 1995 A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems. Zbl 1352.65477 Carey, V.; Estep, D.; Tavener, S. 9 2013 A measure-theoretic computational method for inverse sensitivity problems. III: multiple quantities of interest. Zbl 1351.60084 Butler, T.; Estep, D.; Tavener, S.; Dawson, C.; Westerink, J. J. 9 2014 A computational measure theoretic approach to inverse sensitivity problems. II: A posteriori error analysis. Zbl 1252.60002 Butler, T.; Estep, D.; Sandelin, J. 8 2012 Nonparametric density estimation for randomly perturbed elliptic problems. II: Applications and adaptive modeling. Zbl 1176.76108 Estep, D.; Målqvist, A.; Tavener, S. 8 2009 Applied mathematics: Body and Soul. Vol. 1: Derivatives and geometry in \(\mathbb R^3\). Vol. 2: Integrals and geometry in \(\mathbb R^n\). Vol. 3: Calculus in several dimensions. Zbl 1033.00010 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 8 2004 Fast and reliable methods for determining the evolution of uncertain parameters in differential equations. Zbl 1089.65058 Estep, D.; Neckels, D. 7 2006 An analysis of numerical approximations of metastable solutions of the bistable equation. Zbl 0808.65094 Estep, Donald 7 1994 A posteriori analysis for iterative solvers for nonautonomous evolution problems. Zbl 1322.65063 Chaudhry, J. H.; Estep, D.; Ginting, V.; Tavener, S. 7 2015 The pointwise computability of the Lorenz system. Zbl 0935.65143 Estep, Don; Johnson, Claes 6 1998 Analysis of shear layers in a fluid with temperature-dependent viscosity. Zbl 1044.76031 Estep, Donald J.; Verduyn Lunel, Sjoerd M.; Williams, Roy D. 6 2001 A posteriori error estimation of approximate boundary fluxes. Zbl 1152.65106 Wildey, T.; Tavener, S.; Estep, D. 6 2008 Computational error estimation and adaptive error control for a finite element solution of launch vehicle trajectory problems. Zbl 0956.65051 Estep, Donald; Hodges, Dewey H.; Warner, Michael 5 2000 Applied mathematics: body and soul (Volume 1). Derivatives and geometry in \({\mathbb R}^3\). Transl. by Josef Schüle. (Angewandte Mathematik: Body and soul (Band 1). Ableitungen in Geometrie in \({\mathbb R}^3\). Übersetzt von Josef Schüle.) Zbl 1055.00005 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 5 2004 Accurate parallel integration of large sparse systems of differential equations. Zbl 0862.65041 Estep, Donald J.; Williams, Roy D. 5 1996 A posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with nonmatching. Zbl 1303.65093 Arbogast, T.; Estep, D.; Sheehan, B.; Tavener, S. 5 2014 Efficient distribution estimation and uncertainty quantification for elliptic problems on domains with stochastic boundaries. Zbl 1400.35239 Chaudhry, Jehanzeb H.; Burch, Nathanial; Estep, Donald 5 2018 Using Krylov-subspace iterations in discontinuous Galerkin methods for nonlinear reaction-diffusion systems. Zbl 0946.65079 Estep, Donald J.; Freund, Roland W. 4 2000 The rate of error growth in Hamiltonian-conserving integrators. Zbl 0826.65071 Estep, Donald J.; Stuart, Andrew M. 4 1995 Continuum modeling of large networks. Zbl 1138.90342 Chong, Edwin K. P.; Estep, Donald; Hannig, Jan 3 2008 The solution of a launch vehicle trajectory problem by an adaptive finite element method. Zbl 1007.70021 Estep, Donald J.; Hodges, Dewey H.; Warner, Michael 3 2001 Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations. Zbl 1173.76396 Estep, D.; Neckels, D. 3 2007 Applied mathematics: Body and soul (Volume 2). Integrals and geometry in \({\mathbb R}^3\). Transl. by Josef Schüle. (Angewandte Mathematik: Body and soul (Band 2). Integrale und Geometrie in \({\mathbb R}^3\). Übersetzt von Josef Schüle.) Zbl 1099.00002 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 3 2005 Boundedness of dispersive difference schemes. Zbl 0729.65065 Estep, Donald; Loss, Michael; Rauch, Jeffrey 3 1990 Some stability aspects of schemes for the adaptive integration of stiff initial value problems. Zbl 0738.65072 Dieci, Luca; Estep, Donald 3 1991 Uncertainty quantification for approximate \(p\)-quantiles for physical models with stochastic inputs. Zbl 1311.65003 Elfverson, Daniel; Estep, Donald J.; Hellman, Fredrik; Målqvist, Axel 3 2014 Adaptive finite element solution of multiscale PDE-ODE systems. Zbl 1425.65114 Johansson, A.; Chaudhry, J. H.; Carey, V.; Estep, D.; Ginting, V.; Larson, M.; Tavener, S. 3 2015 A power method for nonlinear operators. Zbl 1141.65037 Eastman, Sean; Estep, Donald 2 2007 A modified equation for dispersive difference schemes. Zbl 0832.65096 Estep, Donald 2 1995 A posteriori error analysis for a cut cell finite volume method. Zbl 1230.76032 Estep, Don; Pernice, Michael; Tavener, Simon; Wang, Haiying 2 2011 The interaction of iteration error and stability for linear partial differential equations coupled through an interface. Zbl 1380.65319 Sheehan, B.; Estep, D.; Tavener, S.; Cary, J.; Kruger, S.; Hakim, A.; Pletzer, A.; Carlsson, J.; Vadlamani, S. 2 2015 Continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations. Zbl 1273.35280 Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; Estep, Donald 2 2013 The formation of shear layers in a fluid with temperature-dependent viscosity. Zbl 1101.76020 Estep, Donald J.; Verduyn Lunel, Sjoerd M.; Williams, Roy D. 1 2005 Nonparametric density estimation for randomly perturbed elliptic problems. III: Convergence, computational cost, and generalizations. Zbl 1295.65007 Estep, Donald; Holst, Michael J.; Målqvist, Axel 1 2012 Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling. Zbl 1294.68037 Burch, Nathanial; Chong, Edwin K. P.; Estep, Don; Hannig, Jan 1 2013 Collected lectures on the preservation of stability under discretization. Lectures presented at the workshop, Colorado State University, Fort Collins, CO, USA, May 30–June 2, 2001. Zbl 1009.00017 1 2002 Adaptive error control during gradient search for an elliptic optimization problem. Zbl 1270.49025 Estep, D.; Lee, S. 1 2013 Error estimation and uncertainty quantification for first time to a threshold value. Zbl 1461.65204 Chaudhry, Jehanzeb H.; Estep, Donald; Stevens, Zachary; Tavener, Simon J. 1 2021 Error estimation and uncertainty quantification for first time to a threshold value. Zbl 1461.65204 Chaudhry, Jehanzeb H.; Estep, Donald; Stevens, Zachary; Tavener, Simon J. 1 2021 Efficient distribution estimation and uncertainty quantification for elliptic problems on domains with stochastic boundaries. Zbl 1400.35239 Chaudhry, Jehanzeb H.; Burch, Nathanial; Estep, Donald 5 2018 A posteriori error analysis of two-stage computation methods with application to efficient discretization and the parareal algorithm. Zbl 1350.65074 Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff 12 2016 A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques. Zbl 1332.65120 Collins, J. B.; Estep, D.; Tavener, S. 13 2015 A posteriori error analysis of IMEX multi-step time integration methods for advection-diffusion-reaction equations. Zbl 1425.65086 Chaudhry, Jehanzeb H.; Estep, Donald; Ginting, Victor; Shadid, John N.; Tavener, Simon 12 2015 A posteriori error estimates for mixed finite element and finite volume methods for parabolic problems coupled through a boundary. Zbl 1322.65093 Arbogast, T.; Estep, D.; Sheehan, B.; Tavener, S. 10 2015 A posteriori analysis for iterative solvers for nonautonomous evolution problems. Zbl 1322.65063 Chaudhry, J. H.; Estep, D.; Ginting, V.; Tavener, S. 7 2015 Adaptive finite element solution of multiscale PDE-ODE systems. Zbl 1425.65114 Johansson, A.; Chaudhry, J. H.; Carey, V.; Estep, D.; Ginting, V.; Larson, M.; Tavener, S. 3 2015 The interaction of iteration error and stability for linear partial differential equations coupled through an interface. Zbl 1380.65319 Sheehan, B.; Estep, D.; Tavener, S.; Cary, J.; Kruger, S.; Hakim, A.; Pletzer, A.; Carlsson, J.; Vadlamani, S. 2 2015 A posteriori error estimation for the Lax-Wendroff finite difference scheme. Zbl 1302.65184 Collins, J. B.; Estep, Don; Tavener, Simon 11 2014 A measure-theoretic computational method for inverse sensitivity problems. III: multiple quantities of interest. Zbl 1351.60084 Butler, T.; Estep, D.; Tavener, S.; Dawson, C.; Westerink, J. J. 9 2014 A posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with nonmatching. Zbl 1303.65093 Arbogast, T.; Estep, D.; Sheehan, B.; Tavener, S. 5 2014 Uncertainty quantification for approximate \(p\)-quantiles for physical models with stochastic inputs. Zbl 1311.65003 Elfverson, Daniel; Estep, Donald J.; Hellman, Fredrik; Målqvist, Axel 3 2014 A posteriori analysis of an iterative multi-discretization method for reaction-diffusion systems. Zbl 1286.65121 Chaudhry, J. H.; Estep, D.; Ginting, V.; Tavener, S. 10 2013 A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems. Zbl 1352.65477 Carey, V.; Estep, D.; Tavener, S. 9 2013 Continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations. Zbl 1273.35280 Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; Estep, Donald 2 2013 Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling. Zbl 1294.68037 Burch, Nathanial; Chong, Edwin K. P.; Estep, Don; Hannig, Jan 1 2013 Adaptive error control during gradient search for an elliptic optimization problem. Zbl 1270.49025 Estep, D.; Lee, S. 1 2013 A posteriori analysis of a multirate numerical method for ordinary differential equations. Zbl 1253.65118 Estep, Donald J.; Ginting, Victor; Tavener, Simon J. 13 2012 A computational measure theoretic approach to inverse sensitivity problems. II: A posteriori error analysis. Zbl 1252.60002 Butler, T.; Estep, D.; Sandelin, J. 8 2012 Nonparametric density estimation for randomly perturbed elliptic problems. III: Convergence, computational cost, and generalizations. Zbl 1295.65007 Estep, Donald; Holst, Michael J.; Målqvist, Axel 1 2012 A measure-theoretic computational method for inverse sensitivity problems. I: Method and analysis. Zbl 1234.60062 Breidt, J.; Butler, T.; Estep, D. 12 2011 A posteriori error analysis for a cut cell finite volume method. Zbl 1230.76032 Estep, Don; Pernice, Michael; Tavener, Simon; Wang, Haiying 2 2011 Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions. Zbl 1216.65127 Carey, V.; Estep, D.; Johansson, A.; Larson, M.; Tavener, S. 12 2010 A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer. Zbl 1281.80004 Estep, Donald; Tavener, Simon; Wildey, Tim 12 2010 Error estimates for multiscale operator decomposition for multiphysics models. Zbl 1218.65100 Estep, D. 11 2010 A posteriori analysis and adaptive error control for multiscale operator decomposition solution of elliptic systems. I: Triangular systems. Zbl 1186.65142 Carey, V.; Estep, D.; Tavener, S. 18 2009 Nonparametric density estimation for randomly perturbed elliptic problems. I: Computational methods, a posteriori analysis, and adaptive error control. Zbl 1194.65128 Estep, D.; Målqvist, A.; Tavener, S. 13 2009 A posteriorierror analysis of a cell-centered finite volume method for semilinear elliptic problems. Zbl 1176.65125 Estep, Don; Pernice, Michael; Pham, Du; Tavener, Simon; Wang, Haiying 12 2009 Nonparametric density estimation for randomly perturbed elliptic problems. II: Applications and adaptive modeling. Zbl 1176.76108 Estep, D.; Målqvist, A.; Tavener, S. 8 2009 An a posteriori-a priori analysis of multiscale operator splitting. Zbl 1166.65367 Estep, D.; Ginting, V.; Ropp, D.; Shadid, J. N.; Tavener, S. 20 2008 A posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem. Zbl 1176.65124 Estep, D.; Tavener, S.; Wildey, T. 11 2008 A posteriori error estimation of approximate boundary fluxes. Zbl 1152.65106 Wildey, T.; Tavener, S.; Estep, D. 6 2008 Continuum modeling of large networks. Zbl 1138.90342 Chong, Edwin K. P.; Estep, Donald; Hannig, Jan 3 2008 Fast methods for determining the evolution of uncertain parameters in reaction-diffusion equations. Zbl 1173.76396 Estep, D.; Neckels, D. 3 2007 A power method for nonlinear operators. Zbl 1141.65037 Eastman, Sean; Estep, Donald 2 2007 Fast and reliable methods for determining the evolution of uncertain parameters in differential equations. Zbl 1089.65058 Estep, D.; Neckels, D. 7 2006 Generalized Green’s functions and the effective domain of influence. Zbl 1078.65095 Estep, Donald; Holst, Michael; Larson, Mats 29 2005 Applied mathematics: Body and soul (Volume 2). Integrals and geometry in \({\mathbb R}^3\). Transl. by Josef Schüle. (Angewandte Mathematik: Body and soul (Band 2). Integrale und Geometrie in \({\mathbb R}^3\). Übersetzt von Josef Schüle.) Zbl 1099.00002 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 3 2005 The formation of shear layers in a fluid with temperature-dependent viscosity. Zbl 1101.76020 Estep, Donald J.; Verduyn Lunel, Sjoerd M.; Williams, Roy D. 1 2005 Applied mathematics: Body and Soul. Vol. 1: Derivatives and geometry in \(\mathbb R^3\). Vol. 2: Integrals and geometry in \(\mathbb R^n\). Vol. 3: Calculus in several dimensions. Zbl 1033.00010 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 8 2004 Applied mathematics: body and soul (Volume 1). Derivatives and geometry in \({\mathbb R}^3\). Transl. by Josef Schüle. (Angewandte Mathematik: Body and soul (Band 1). Ableitungen in Geometrie in \({\mathbb R}^3\). Übersetzt von Josef Schüle.) Zbl 1055.00005 Eriksson, Kenneth; Estep, Donald; Johnson, Claes 5 2004 Accounting for stability: A posteriori error estimates based on residuals and variational analysis. Zbl 0994.65097 Estep, Donald; Holst, Michael; Mikulencak, Duane 13 2002 The dynamical behavior of the discontinuous Galerkin method and related difference schemes. Zbl 0998.65080 Estep, Donald J.; Stuart, Andrew M. 12 2002 Practical analysis in one variable. Zbl 1038.26001 Estep, Donald 11 2002 Collected lectures on the preservation of stability under discretization. Lectures presented at the workshop, Colorado State University, Fort Collins, CO, USA, May 30–June 2, 2001. Zbl 1009.00017 1 2002 Analysis of shear layers in a fluid with temperature-dependent viscosity. Zbl 1044.76031 Estep, Donald J.; Verduyn Lunel, Sjoerd M.; Williams, Roy D. 6 2001 The solution of a launch vehicle trajectory problem by an adaptive finite element method. Zbl 1007.70021 Estep, Donald J.; Hodges, Dewey H.; Warner, Michael 3 2001 Estimating the error of numerical solutions of systems of reaction-diffusion equations. Zbl 0998.65096 Estep, Donald J.; Larson, Mats G.; Williams, Roy D. 59 2000 Computational error estimation and adaptive error control for a finite element solution of launch vehicle trajectory problems. Zbl 0956.65051 Estep, Donald; Hodges, Dewey H.; Warner, Michael 5 2000 Using Krylov-subspace iterations in discontinuous Galerkin methods for nonlinear reaction-diffusion systems. Zbl 0946.65079 Estep, Donald J.; Freund, Roland W. 4 2000 The pointwise computability of the Lorenz system. Zbl 0935.65143 Estep, Don; Johnson, Claes 6 1998 Computational differential equations. Zbl 0946.65049 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 95 1996 Accurate parallel integration of large sparse systems of differential equations. Zbl 0862.65041 Estep, Donald J.; Williams, Roy D. 5 1996 Introduction to adaptive methods for differential equations. Zbl 0829.65122 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 217 1995 A posteriori error bounds and global error control for approximation of ordinary differential equations. Zbl 0820.65052 Estep, Donald 79 1995 \(h\)-adaptive boundary element schemes. Zbl 0821.65072 Carstensen, C.; Estep, Donald; Stephan, P. 9 1995 Introduction to computational methods for differential equations. Zbl 0843.65057 Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes 9 1995 The rate of error growth in Hamiltonian-conserving integrators. Zbl 0826.65071 Estep, Donald J.; Stuart, Andrew M. 4 1995 A modified equation for dispersive difference schemes. Zbl 0832.65096 Estep, Donald 2 1995 Global error control for the continuous Galerkin finite element method for ordinary differential equations. Zbl 0822.65054 Estep, Donald; French, Donald 38 1994 An analysis of numerical approximations of metastable solutions of the bistable equation. Zbl 0808.65094 Estep, Donald 7 1994 The discontinuous Galerkin method for semilinear parabolic problems. Zbl 0768.65065 Estep, Donald; Larsson, S. 19 1993 Some stability aspects of schemes for the adaptive integration of stiff initial value problems. Zbl 0738.65072 Dieci, Luca; Estep, Donald 3 1991 Boundedness of dispersive difference schemes. Zbl 0729.65065 Estep, Donald; Loss, Michael; Rauch, Jeffrey 3 1990 all cited Publications top 5 cited Publications all top 5 Cited by 874 Authors 35 Estep, Donald J. 24 Tavener, Simon J. 20 Carstensen, Carsten 15 Chaudhry, Jehanzeb Hameed 12 Beilina, Larisa 12 Hoffman, Johan 12 Larson, Mats G. 11 Houston, Paul 11 Larsson, Fredrik 10 Becker, Roland 10 Hoppe, Ronald H. W. 10 Rannacher, Rolf 8 Mahnken, Rolf 8 Runesson, Kenneth 8 van der Zee, Kristoffer George 8 Vexler, Boris 8 Wihler, Thomas Pascal 7 Praetorius, Dirk 7 Shadid, John N. 7 Whiteley, Jonathan P. 6 Carey, Graham Francis 6 Chrysafinos, Konstantinos 6 Ginting, Victor 6 Hauke, Guillermo 6 Johnson, Claes G. L. 6 Makridakis, Charalambos G. 6 Prudhomme, Serge 6 Van Brummelen, Harald 5 Baccouch, Mahboub 5 Bengzon, Fredrik 5 Butler, Troy D. 5 Feistauer, Miloslav 5 Funken, Stefan A. 5 Jansson, Johan 5 Korotov, Sergey 5 Logg, Anders 5 Målqvist, Axel 5 Mattis, Steven A. 5 Rüter, Marcus Olavi 5 Stein, Erwin 5 Whiteman, John Robert 5 Wick, Thomas 4 Akrivis, Georgios D. 4 Arshad, Muhammad 4 Bartels, Sören 4 Collins, Joseph B. 4 Dawson, Clint N. 4 Díez, Pedro 4 French, Donald A. 4 Holst, Michael J. 4 Innerberger, Michael 4 Irisarri, Diego 4 John, Volker 4 Ju, Xiaozhe 4 Katsaounis, Theodoros 4 Liu, Jiangguo 4 Lötstedt, Per 4 Matthies, Gunar 4 Nochetto, Ricardo Horacio 4 Repin, Sergeĭ Igorevich 4 Reynolds, Daniel R. 4 Szepessy, Anders 4 Tempone, Raúl F. 4 Tzavaras, Athanasios E. 4 Wollner, Winnifried 4 Yi, Lijun 3 Asadzadeh, Mohammad Sina 3 Berrone, Stefano 3 Bespalov, Alexei 3 Betsch, Peter 3 Carey, Varis 3 Chinomona, Rujeko 3 Cliffe, K. Andrew 3 Cockburn, Bernardo 3 Gainova, Irina 3 Georgoulis, Emmanuil H. 3 Gross, Michael B. 3 Hall, Edward J. C. 3 Hannig, Jan 3 Jakeman, John Davis 3 Johansson, Håkan 3 Karátson, János 3 Klibanov, Michael V. 3 Mao, Shipeng 3 Mavriplis, Dimitri J. 3 Meidner, Dominik 3 Metcalfe, Stephen 3 Nazarov, Murtazo 3 Parés, Núria 3 Pernice, Michael 3 Pollock, Sara 3 Rocchi, Leonardo 3 Shi, Dongyang 3 Stuart, Andrew M. 3 Süli, Endre E. 3 Verdugo, Francesc 3 Vilela De Abreu, Rodrigo 3 Woodward, Carol S. 3 Yang, Huaijun 3 Zhong, Hongzhi ...and 774 more Authors all top 5 Cited in 132 Serials 82 Computer Methods in Applied Mechanics and Engineering 40 Journal of Computational Physics 33 Journal of Computational and Applied Mathematics 27 Numerische Mathematik 26 Applied Numerical Mathematics 22 International Journal for Numerical Methods in Engineering 21 Journal of Scientific Computing 21 SIAM Journal on Scientific Computing 17 Computational Mechanics 14 Mathematics of Computation 13 BIT 12 Computers & Mathematics with Applications 11 SIAM/ASA Journal on Uncertainty Quantification 10 Numerical Methods for Partial Differential Equations 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Communications in Numerical Methods in Engineering 7 International Journal for Numerical Methods in Fluids 7 Applied Mathematics and Computation 7 Applications of Mathematics 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Computational Methods in Applied Mathematics 6 Mathematics and Computers in Simulation 6 SIAM Journal on Numerical Analysis 6 Journal of Numerical Mathematics 4 Numerical Algorithms 4 Advances in Computational Mathematics 3 Journal of Mathematical Analysis and Applications 3 Journal of Mathematical Biology 3 Computing 3 Computational Optimization and Applications 3 Journal of Mathematical Sciences (New York) 3 Engineering Analysis with Boundary Elements 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Computational Geosciences 3 Journal of Applied Mathematics and Computing 3 International Journal of Numerical Analysis and Modeling 2 Applicable Analysis 2 Mathematical Biosciences 2 Calcolo 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Applied Mathematics Letters 2 SIAM Journal on Matrix Analysis and Applications 2 Neural Networks 2 Computational Mathematics and Mathematical Physics 2 Applied Mathematical Modelling 2 SIAM Review 2 Annales Mathématiques Blaise Pascal 2 Computational and Applied Mathematics 2 Computing and Visualization in Science 2 International Journal of Computational Fluid Dynamics 2 Abstract and Applied Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Archives of Computational Methods in Engineering 2 GAMM-Mitteilungen 2 International Journal for Numerical Methods in Biomedical Engineering 2 Journal of Applied Nonlinear Dynamics 1 Archive for Rational Mechanics and Analysis 1 Computers and Fluids 1 Communications on Pure and Applied Mathematics 1 International Journal of Control 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Mechanics and Physics of Solids 1 Mathematical Methods in the Applied Sciences 1 Scandinavian Journal of Statistics 1 Transport Theory and Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Optimization Theory and Applications 1 Kyungpook Mathematical Journal 1 Studies in Applied Mathematics 1 Applied Mathematics and Mechanics. (English Edition) 1 Journal of Computational Mathematics 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Acta Mathematicae Applicatae Sinica. English Series 1 Asia-Pacific Journal of Operational Research 1 MCSS. Mathematics of Control, Signals, and Systems 1 Science in China. Series A 1 The Annals of Applied Probability 1 Journal of Global Optimization 1 International Journal of Computer Mathematics 1 SIAM Journal on Applied Mathematics 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 Indagationes Mathematicae. New Series 1 Archive of Applied Mechanics 1 SIAM Journal on Optimization 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 Journal of Convex Analysis 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Inequalities and Applications 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 International Journal of Theoretical and Applied Finance 1 European Journal of Mechanics. B. Fluids 1 Acta Mathematica Sinica. English Series ...and 32 more Serials all top 5 Cited in 33 Fields 470 Numerical analysis (65-XX) 206 Partial differential equations (35-XX) 119 Fluid mechanics (76-XX) 100 Mechanics of deformable solids (74-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 38 Ordinary differential equations (34-XX) 24 Probability theory and stochastic processes (60-XX) 22 Biology and other natural sciences (92-XX) 16 Classical thermodynamics, heat transfer (80-XX) 15 Statistics (62-XX) 15 Optics, electromagnetic theory (78-XX) 13 Dynamical systems and ergodic theory (37-XX) 13 Integral equations (45-XX) 10 Operations research, mathematical programming (90-XX) 9 Geophysics (86-XX) 8 Mechanics of particles and systems (70-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Approximations and expansions (41-XX) 6 Computer science (68-XX) 6 Systems theory; control (93-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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