Edit Profile (opens in new tab) Luskin, Mitchell Co-Author Distance Author ID: luskin.mitchell Published as: Luskin, Mitchell; Luskin, M. Documents Indexed: 122 Publications since 1979, including 7 Additional arXiv Preprints 5 Contributions as Editor Co-Authors: 81 Co-Authors with 113 Joint Publications 2,878 Co-Co-Authors all top 5 Co-Authors 13 single-authored 15 Ortner, Christoph 10 Bělík, Pavel 8 Dobson, Matthew 8 Margetis, Dionisios 6 Li, Xingjie Helen 6 Maier, Matthias Sebastian 6 Massatt, Daniel 6 Shapeev, Alexander V. 6 Watson, Alexander B. 5 Li, Bo 4 Cazeaux, Paul 4 Collins, Charles R. 4 Vankoten, Brian 3 Arndt, Marcel 3 Bochev, Pavel B. 3 Carr, Stephen H. 3 Chipot, Michel 3 Kheshgi, Haroon S. 3 Kinderlehrer, David 3 Klouček, Petr 3 Olson, Derek 3 Perez, Danny 3 Simpson, Gideon 3 Temple, Blake 2 Binder, Andrew J. 2 Cockburn, Bernardo 2 Descloux, Jean 2 Kong, Tianyu 2 Legoll, Frédéric 2 Moeckel, Richard 2 Rannacher, Rolf 2 Sell, George Roger 2 Shu, Chi-Wang 2 Song, Jung Heon 2 Süli, Endre E. 2 Tadmor, Ellad B. 1 Bal, Guillaume 1 Bern, Marshall W. 1 Bhattacharya, Kaushik 1 Bjørstad, Petter Erling 1 Brule, Timothy 1 Cancès, Eric 1 Clark, Drake 1 Efendiev, Yalchin R. 1 Engelke, Rebecca 1 Engquist, Bjorn E. 1 Ericksen, Jerald Laverne 1 Etter, Simon 1 Fabes, Eugene B. 1 Farmer, Brittan A 1 Flaherty, Joseph E. 1 Golub, Gene Howard 1 Greenbaum, Anne 1 Hardt, Robert M. 1 Hott, Michael 1 James, Richard D. 1 Kaxiras, Efthimios 1 Kim, Philip 1 Kim, Woo Kyun 1 Kružík, Martin 1 Le Bris, Claude 1 Lelièvre, Tony 1 Lin, Sanyih 1 Liu, Diyi 1 Lorence, Leonard J. jun. 1 Low, Tony 1 Lucas, Andrew 1 Ma, Ling 1 Macdonald, Allan H. 1 Majda, Andrew J. 1 Martin, William R. 1 Mattheakis, Marios 1 Pan, Tsorng-Whay 1 Plecháč, Petr 1 Rappaz, Jacques 1 Riordan, James 1 Rybka, Piotr 1 Srolovitz, David J. 1 Stauber, Tobias 1 Voter, Arthur F. 1 Zhang, Tianyu all top 5 Serials 14 Multiscale Modeling & Simulation 12 SIAM Journal on Numerical Analysis 8 Mathematics of Computation 6 Computer Methods in Applied Mechanics and Engineering 5 Journal of Mathematical Physics 5 The IMA Volumes in Mathematics and its Applications 4 Archive for Rational Mechanics and Analysis 4 SIAM Journal on Mathematical Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Journal of the Mechanics and Physics of Solids 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Journal of Computational Physics 2 Studies in Applied Mathematics 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Non-Newtonian Fluid Mechanics 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 IMA Journal of Numerical Analysis 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Calcolo 1 Journal of Differential Equations 1 Numerische Mathematik 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Japan Journal of Industrial and Applied Mathematics 1 Journal of Elasticity 1 SIAM Journal on Applied Mathematics 1 Continuum Mechanics and Thermodynamics 1 Monte Carlo Methods and Applications 1 Interfaces and Free Boundaries 1 Communications in Mathematical Sciences 1 Acta Numerica 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Journal of Physics A: Mathematical and Theoretical 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 62 Numerical analysis (65-XX) 50 Mechanics of deformable solids (74-XX) 47 Statistical mechanics, structure of matter (82-XX) 27 Partial differential equations (35-XX) 18 Fluid mechanics (76-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Mechanics of particles and systems (70-XX) 11 Optics, electromagnetic theory (78-XX) 9 Quantum theory (81-XX) 5 General and overarching topics; collections (00-XX) 5 Dynamical systems and ergodic theory (37-XX) 3 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 1,259 times in 759 Documents Cited by ▼ Year ▼ Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049 Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 95 2003 On the computation of crystalline microstructure. Zbl 0867.65033 Luskin, Mitchell 64 1996 On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064 Luskin, Mitchell; Rannacher, Rolf 60 1982 Atomistic-to-continuum coupling. Zbl 1464.74007 Luskin, Mitchell; Ortner, Christoph 51 2013 On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062 Luskin, Mitchell; Rannacher, Rolf 41 1982 A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059 Luskin, Mitchell 37 1979 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054 Luskin, Mitchell; Temple, Blake 30 1982 Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006 Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph 29 2010 Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006 Dobson, Matthew; Luskin, Mitchell 24 2008 A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045 Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny 24 2012 Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123 Luskin, M.; Ortner, C.; Van Koten, B. 24 2013 Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002 Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 22 2007 Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067 Collins, Charles; Kinderlehrer, David; Luskin, Mitchell 22 1991 Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081 Klouček, Petr; Li, Bo; Luskin, Mitchell 21 1996 An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089 Dobson, Matthew; Luskin, Mitchell 21 2009 Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047 Fabes, Eugene; Luskin, Mitchell; Sell, George R. 20 1991 The computation of the austenitic-martensitic phase transition. Zbl 0991.80502 Collins, Charles; Luskin, Mitchell 20 1989 An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122 Luskin, Mitchell; Ortner, Christoph 20 2009 An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414 Dobson, Matthew; Luskin, Mitchell 19 2009 Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313 Arndt, Marcel; Luskin, Mitchell 19 2008 Relaxation methods for liquid crystal problems. Zbl 0685.65058 Lin, San-Yih; Luskin, Mitchell 18 1989 Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014 Rybka, Piotr; Luskin, Mitchell 18 2005 The computation of the dynamics of the martensitic transformation. Zbl 0825.73047 Klouček, P.; Luskin, M. 18 1994 Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009 Dobson, M.; Luskin, M.; Ortner, C. 18 2010 The simply laminated microstructure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation. Zbl 0942.74056 Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell 17 1999 Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113 Luskin, Mitchell; Ma, Ling 17 1992 An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220 Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V. 17 2014 Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085 Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 16 2000 Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026 Van Koten, Brian; Luskin, Mitchell 16 2011 Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004 Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V. 16 2014 Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005 Dobson, M.; Luskin, M.; Ortner, C. 16 2010 Approximation theories for inertial manifolds. Zbl 0688.58035 Luskin, Mitchell; Sell, George R. 15 1989 The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039 Kružík, Martin; Luskin, Mitchell 15 2003 Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012 Arndt, Marcel; Luskin, Mitchell 15 2008 Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084 Chipot, Michel; Luskin, Mitchell 14 1986 On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014 Luskin, Mitchell 14 1981 Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem. Zbl 0735.65042 Collins, Charles; Luskin, Mitchell 14 1991 Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076 Li, Bo; Luskin, Mitchell 13 1998 Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066 Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 13 2009 Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048 Collins, Charles; Luskin, Mitchell; Riordan, James 12 1993 Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099 Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell 12 2017 A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078 Li, Xingjie Helen; Luskin, Mitchell 11 2012 Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060 Luskin, Mitchell 11 1996 Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020 Li, Bo; Luskin, Mitchell 10 1998 Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107 Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 10 2012 Approximation of the spectrum of closed operators: The determination of normal modes of a rotating basin. Zbl 0458.65084 Descloux, Jean; Luskin, Mitchell; Rappaz, Jacques 9 1981 Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037 Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 9 2017 Electronic density of states for incommensurate layers. Zbl 1365.81164 Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 9 2017 Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222 Dobson, M.; Luskin, M.; Ortner, C. 8 2011 Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012 Li, Bo; Luskin, Mitchell 8 1999 Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015 Cohen, Robert; Luskin, Mitchell 8 1991 Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics. Zbl 1303.74007 Kim, W. K.; Luskin, M.; Perez, D.; Voter, A. F.; Tadmor, E. B. 8 2014 A computational and theoretical investigation of the accuracy of quasicontinuum methods. Zbl 1245.74102 Van Koten, Brian; Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 7 2012 Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085 Dobson, Matthew; Luskin, Mitchell 7 2008 A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013 Bělík, Pavel; Luskin, Mitchell 7 2002 Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328 Luskin, Mitchell; Zhang, Tianyu 7 2007 Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064 Klouček, P.; Luskin, M. 7 1994 Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042 Bělík, Pavel; Luskin, Mitchell 6 2000 Incommensurate heterostructures in momentum space. Zbl 1434.82101 Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph 6 2018 Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020 Bělík, Pavel; Luskin, Mitchell 6 2003 Approximation of crystalline defects at finite temperature. Zbl 1378.82046 Shapeev, Alexander V.; Luskin, Mitchell 6 2017 A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059 Bělík, Pavel; Luskin, Mitchell 6 2002 Existence of the first magic angle for the chiral model of bilayer graphene. Zbl 1506.82045 Watson, Alexander B.; Luskin, Mitchell 6 2021 Energy minimization of two dimensional incommensurate heterostructures. Zbl 1433.74051 Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel 6 2020 Parallel solution of partial differential equations. Proceedings of a workshop, Univ. of Minnesota, Minneapolis, MN, USA, June 9–13, 1997. Zbl 0938.00013 5 2000 On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047 Bělík, Pavel; Brule, Timothy; Luskin, Mitchell 5 2001 Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053 Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell 5 1988 Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. Zbl 1353.82022 Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; Luskin, Mitchell 5 2016 Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018 Song, Jung Heon; Maier, Matthias; Luskin, Mitchell 5 2019 A finite element method for first-order hyperbolic systems. Zbl 0447.65064 Luskin, Mitchell 4 1980 On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006 Margetis, Dionisios; Luskin, Mitchell 4 2016 Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022 Cazeaux, Paul; Luskin, Mitchell; Tadmor, Ellad B. 4 2017 Numerical analysis of parallel replica dynamics. Zbl 1298.65016 Simpson, Gideon; Luskin, Mitchell 4 2013 Bistritzer-Macdonald dynamics in twisted bilayer graphene. Zbl 1511.82042 Watson, Alexander B.; Kong, Tianyu; MacDonald, Allan H.; Luskin, Mitchell 4 2023 Modeling and computation of Kubo conductivity for two-dimensional incommensurate bilayers. Zbl 1460.65039 Etter, Simon; Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 4 2020 The \(\Gamma\)-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013 Belík, Pavel; Luskin, Mitchell 3 2007 Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044 Kheshgi, Haroon; Luskin, Mitchell 3 1985 An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086 Luskin, Mitchell 3 1979 Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061 Luskin, M. 3 1991 Computational modeling of microstructure. Zbl 1025.49014 Luskin, Mitchell 3 2002 Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009 Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D. 3 2019 Efficient computation of Kubo conductivity for incommensurate 2D heterostructures. Zbl 1516.82119 Massatt, Daniel; Carr, Stephen; Luskin, Mitchell 3 2020 Computational modeling of softening in a structural phase transformation. Zbl 1108.74045 Bělík, Pavel; Luskin, Mitchell 2 2005 A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046 Bělík, Pavel; Luskin, Mitchell 2 2004 Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019 Luskin, Mitchell; Pan, Tsorng-Whay 2 1992 Convergence of a finite element method for the approximation of normal modes of the oceans. Zbl 0431.65066 Luskin, Mitchell 2 1979 On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009 Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell 2 2017 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063 Luskin, Mitchell; Temple, Blake 1 1982 On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037 Kheshgi, Haroon; Luskin, Mitchell 1 1983 On the classification of some model equations for viscoelasticity. Zbl 0559.76011 Luskin, Mitchell 1 1984 Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042 Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 1 2018 On the stability of microstructure for general martensitic transformations. Zbl 1049.74737 Luskin, M. 1 2000 Grid generation and adaptive algorithms. Proceedings of a workshop, integral part of 1996-97 IMA program, Minnesota Univ., Minneapolis, MN, USA, April 28 - May 2, 1997. Zbl 0932.00052 1 1999 A finite element model for martensitic thin films. Zbl 1168.65308 Bělík, Pavel; Luskin, Mitchell 1 2006 A theoretical examination of diffusive molecular dynamics. Zbl 1354.82015 Simpson, G.; Luskin, M.; Srolovitz, D. J. 1 2016 Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1D. Zbl 1362.74009 Binder, Andrew J.; Luskin, Mitchell; Ortner, Christoph 1 2017 Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004 Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F. 1 2015 On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform. Zbl 07771114 Margetis, Dionisios; Watson, Alexander B.; Luskin, Mitchell 1 2023 Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075 Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V. 1 2014 Stability and convergence of the string method for computing minimum energy paths. Zbl 07107075 Van Koten, Brian; Luskin, Mitchell 1 2019 Bistritzer-Macdonald dynamics in twisted bilayer graphene. Zbl 1511.82042 Watson, Alexander B.; Kong, Tianyu; MacDonald, Allan H.; Luskin, Mitchell 4 2023 On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform. Zbl 07771114 Margetis, Dionisios; Watson, Alexander B.; Luskin, Mitchell 1 2023 Existence of the first magic angle for the chiral model of bilayer graphene. Zbl 1506.82045 Watson, Alexander B.; Luskin, Mitchell 6 2021 Energy minimization of two dimensional incommensurate heterostructures. Zbl 1433.74051 Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel 6 2020 Modeling and computation of Kubo conductivity for two-dimensional incommensurate bilayers. Zbl 1460.65039 Etter, Simon; Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 4 2020 Efficient computation of Kubo conductivity for incommensurate 2D heterostructures. Zbl 1516.82119 Massatt, Daniel; Carr, Stephen; Luskin, Mitchell 3 2020 Nonlinear eigenvalue problems for coupled Helmholtz equations modeling gradient-index graphene waveguides. Zbl 07508434 Song, Jung Heon; Maier, Matthias; Luskin, Mitchell 1 2020 Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018 Song, Jung Heon; Maier, Matthias; Luskin, Mitchell 5 2019 Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009 Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D. 3 2019 Stability and convergence of the string method for computing minimum energy paths. Zbl 07107075 Van Koten, Brian; Luskin, Mitchell 1 2019 Incommensurate heterostructures in momentum space. Zbl 1434.82101 Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph 6 2018 Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042 Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 1 2018 Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099 Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell 12 2017 Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037 Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 9 2017 Electronic density of states for incommensurate layers. Zbl 1365.81164 Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 9 2017 Approximation of crystalline defects at finite temperature. Zbl 1378.82046 Shapeev, Alexander V.; Luskin, Mitchell 6 2017 Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022 Cazeaux, Paul; Luskin, Mitchell; Tadmor, Ellad B. 4 2017 On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009 Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell 2 2017 Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1D. Zbl 1362.74009 Binder, Andrew J.; Luskin, Mitchell; Ortner, Christoph 1 2017 Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. Zbl 1353.82022 Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; Luskin, Mitchell 5 2016 On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006 Margetis, Dionisios; Luskin, Mitchell 4 2016 A theoretical examination of diffusive molecular dynamics. Zbl 1354.82015 Simpson, G.; Luskin, M.; Srolovitz, D. J. 1 2016 Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004 Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F. 1 2015 An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220 Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V. 17 2014 Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004 Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V. 16 2014 Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics. Zbl 1303.74007 Kim, W. K.; Luskin, M.; Perez, D.; Voter, A. F.; Tadmor, E. B. 8 2014 Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075 Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V. 1 2014 Atomistic-to-continuum coupling. Zbl 1464.74007 Luskin, Mitchell; Ortner, Christoph 51 2013 Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123 Luskin, M.; Ortner, C.; Van Koten, B. 24 2013 Numerical analysis of parallel replica dynamics. Zbl 1298.65016 Simpson, Gideon; Luskin, Mitchell 4 2013 A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045 Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny 24 2012 A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078 Li, Xingjie Helen; Luskin, Mitchell 11 2012 Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107 Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 10 2012 A computational and theoretical investigation of the accuracy of quasicontinuum methods. Zbl 1245.74102 Van Koten, Brian; Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 7 2012 Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026 Van Koten, Brian; Luskin, Mitchell 16 2011 Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222 Dobson, M.; Luskin, M.; Ortner, C. 8 2011 Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006 Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph 29 2010 Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009 Dobson, M.; Luskin, M.; Ortner, C. 18 2010 Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005 Dobson, M.; Luskin, M.; Ortner, C. 16 2010 An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089 Dobson, Matthew; Luskin, Mitchell 21 2009 An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122 Luskin, Mitchell; Ortner, Christoph 20 2009 An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414 Dobson, Matthew; Luskin, Mitchell 19 2009 Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066 Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 13 2009 Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006 Dobson, Matthew; Luskin, Mitchell 24 2008 Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313 Arndt, Marcel; Luskin, Mitchell 19 2008 Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012 Arndt, Marcel; Luskin, Mitchell 15 2008 Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085 Dobson, Matthew; Luskin, Mitchell 7 2008 Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002 Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 22 2007 Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328 Luskin, Mitchell; Zhang, Tianyu 7 2007 The \(\Gamma\)-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013 Belík, Pavel; Luskin, Mitchell 3 2007 A finite element model for martensitic thin films. Zbl 1168.65308 Bělík, Pavel; Luskin, Mitchell 1 2006 Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014 Rybka, Piotr; Luskin, Mitchell 18 2005 Computational modeling of softening in a structural phase transformation. Zbl 1108.74045 Bělík, Pavel; Luskin, Mitchell 2 2005 A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046 Bělík, Pavel; Luskin, Mitchell 2 2004 Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049 Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 95 2003 The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039 Kružík, Martin; Luskin, Mitchell 15 2003 Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020 Bělík, Pavel; Luskin, Mitchell 6 2003 A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013 Bělík, Pavel; Luskin, Mitchell 7 2002 A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059 Bělík, Pavel; Luskin, Mitchell 6 2002 Computational modeling of microstructure. Zbl 1025.49014 Luskin, Mitchell 3 2002 On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047 Bělík, Pavel; Brule, Timothy; Luskin, Mitchell 5 2001 Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085 Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 16 2000 Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042 Bělík, Pavel; Luskin, Mitchell 6 2000 Parallel solution of partial differential equations. Proceedings of a workshop, Univ. of Minnesota, Minneapolis, MN, USA, June 9–13, 1997. Zbl 0938.00013 5 2000 On the stability of microstructure for general martensitic transformations. Zbl 1049.74737 Luskin, M. 1 2000 The simply laminated microstructure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation. Zbl 0942.74056 Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell 17 1999 Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012 Li, Bo; Luskin, Mitchell 8 1999 Grid generation and adaptive algorithms. Proceedings of a workshop, integral part of 1996-97 IMA program, Minnesota Univ., Minneapolis, MN, USA, April 28 - May 2, 1997. Zbl 0932.00052 1 1999 Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076 Li, Bo; Luskin, Mitchell 13 1998 Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020 Li, Bo; Luskin, Mitchell 10 1998 On the computation of crystalline microstructure. Zbl 0867.65033 Luskin, Mitchell 64 1996 Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081 Klouček, Petr; Li, Bo; Luskin, Mitchell 21 1996 Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060 Luskin, Mitchell 11 1996 The computation of the dynamics of the martensitic transformation. Zbl 0825.73047 Klouček, P.; Luskin, M. 18 1994 Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064 Klouček, P.; Luskin, M. 7 1994 Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048 Collins, Charles; Luskin, Mitchell; Riordan, James 12 1993 Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113 Luskin, Mitchell; Ma, Ling 17 1992 Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019 Luskin, Mitchell; Pan, Tsorng-Whay 2 1992 Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067 Collins, Charles; Kinderlehrer, David; Luskin, Mitchell 22 1991 Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047 Fabes, Eugene; Luskin, Mitchell; Sell, George R. 20 1991 Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem. Zbl 0735.65042 Collins, Charles; Luskin, Mitchell 14 1991 Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015 Cohen, Robert; Luskin, Mitchell 8 1991 Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061 Luskin, M. 3 1991 The computation of the austenitic-martensitic phase transition. Zbl 0991.80502 Collins, Charles; Luskin, Mitchell 20 1989 Relaxation methods for liquid crystal problems. Zbl 0685.65058 Lin, San-Yih; Luskin, Mitchell 18 1989 Approximation theories for inertial manifolds. Zbl 0688.58035 Luskin, Mitchell; Sell, George R. 15 1989 Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053 Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell 5 1988 Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084 Chipot, Michel; Luskin, Mitchell 14 1986 Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044 Kheshgi, Haroon; Luskin, Mitchell 3 1985 On the classification of some model equations for viscoelasticity. Zbl 0559.76011 Luskin, Mitchell 1 1984 On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037 Kheshgi, Haroon; Luskin, Mitchell 1 1983 On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064 Luskin, Mitchell; Rannacher, Rolf 60 1982 On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062 Luskin, Mitchell; Rannacher, Rolf 41 1982 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054 Luskin, Mitchell; Temple, Blake 30 1982 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063 Luskin, Mitchell; Temple, Blake 1 1982 On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014 Luskin, Mitchell 14 1981 Approximation of the spectrum of closed operators: The determination of normal modes of a rotating basin. Zbl 0458.65084 Descloux, Jean; Luskin, Mitchell; Rappaz, Jacques 9 1981 A finite element method for first-order hyperbolic systems. Zbl 0447.65064 Luskin, Mitchell 4 1980 A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059 Luskin, Mitchell 37 1979 An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086 Luskin, Mitchell 3 1979 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 986 Authors 51 Luskin, Mitchell 39 Ortner, Christoph 27 Ryan, Jennifer K. 16 Kružík, Martin 15 Carstensen, Carsten 13 Kirby, Robert M. II 11 Wang, Junjun 11 Zhang, Lei 10 Bartels, Sören 10 Shi, Dongyang 9 Chen, Huajie 9 Lelièvre, Tony 9 Roubíček, Tomáš 9 Shapeev, Alexander V. 9 Shi, Zhongci 9 Sinha, Rajen Kumar 8 Klouček, Petr 8 Li, Zhiping 7 Basaran, Osman A. 7 Li, Xiaozhou 7 Li, Xingjie Helen 7 Lin, Ping 7 Margetis, Dionisios 7 Ming, Pingbing 7 Nochetto, Ricardo Horacio 7 Stefanelli, Ulisse 7 Wang, Yangshuai 6 Bělík, Pavel 6 Bochev, Pavel B. 6 Cockburn, Bernardo 6 Dobson, Matthew 6 Leimkuhler, Benedict J. 6 Li, Xiantao 6 Liao, Mingjie 6 Massatt, Daniel 6 Nectoux, Boris 6 Pedregal, Pablo 6 Plecháč, Petr 6 Sell, George Roger 6 Shu, Chi-Wang 6 Titi, Edriss Saleh 6 Walker, Shawn W. 6 Wang, Hao 6 Zhang, Zhimin 5 Cazeaux, Paul 5 Chipot, Michel 5 Hackl, Klaus 5 Hong, John Meng-Kai 5 Ji, Liangyue 5 Lu, Jianfeng 5 Maier, Matthias Sebastian 5 Mao, Shipeng 5 Ortiz, Michael 4 Azaïez, Mejdi 4 Baccouch, Mahboub 4 Braun, Julian 4 Bresciani, Marco 4 Butler, Leo T. 4 Conti, Sergio 4 Dolzmann, Georg 4 Jolly, Michael Summerfield 4 Khaliq, Abdul Q. M. 4 Kinderlehrer, David 4 Le Peutrec, Dorian 4 Legoll, Frédéric 4 Li, Jichun 4 Li, Meng 4 Meng, Xiong 4 Miehe, Christian 4 Mirzaee, Hanieh 4 Nakao, Mitsuhiro T. 4 Olson, Derek 4 Pan, Ronghua 4 Peerlings, Ron H. J. 4 Praetorius, Dirk 4 Prohl, Andreas 4 Qiu, Jingmei 4 Shao, Zhiqiang 4 Theil, Florian 4 To, Albert C. 4 Vankoten, Brian 4 Vuik, Cornelis 4 Watson, Alexander B. 4 Xu, Yan 4 Yang, Qingcheng 4 Yang, Xiaozhong 4 Zhou, Zhi 3 Ahusborde, Etienne 3 Aristoff, David 3 Beex, Lars A. A. 3 Benešová, Barbora 3 Bhattacharya, Kaushik 3 Binder, Andrew J. 3 Biyikli, Emre 3 Bonfoh, Ahmed S. 3 Cancès, Eric 3 Cang, Shijian 3 Carr, Stephen H. 3 Chen, Zengqiang 3 Cheng, Yingda ...and 886 more Authors all top 5 Cited in 171 Serials 49 Computer Methods in Applied Mechanics and Engineering 43 Journal of Scientific Computing 31 Journal of Computational Physics 31 Mathematics of Computation 24 Archive for Rational Mechanics and Analysis 23 Multiscale Modeling & Simulation 21 Journal of the Mechanics and Physics of Solids 19 Journal of Computational and Applied Mathematics 19 Numerische Mathematik 19 Applied Numerical Mathematics 16 SIAM Journal on Numerical Analysis 15 Journal of Mathematical Analysis and Applications 14 Computers & Mathematics with Applications 14 Journal of Differential Equations 14 SIAM Journal on Scientific Computing 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 11 Numerical Methods for Partial Differential Equations 11 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Continuum Mechanics and Thermodynamics 8 Journal of Statistical Physics 8 Applied Mathematics and Computation 8 Numerical Functional Analysis and Optimization 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Communications in Computational Physics 7 Computers and Fluids 7 Physica D 7 RAIRO. Modélisation Mathématique et Analyse Numérique 7 SIAM Journal on Mathematical Analysis 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 7 Communications on Applied Mathematics and Computation 6 Journal of Mathematical Physics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 International Journal for Numerical Methods in Engineering 6 Physics of Fluids 5 Applicable Analysis 5 Calcolo 5 Mathematical and Computer Modelling 5 Computational and Applied Mathematics 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Science China. Mathematics 4 GAMM-Mitteilungen 3 Communications on Pure and Applied Mathematics 3 Chaos, Solitons and Fractals 3 BIT 3 Computing 3 SIAM Journal on Control and Optimization 3 Science in China. Series A 3 Japan Journal of Industrial and Applied Mathematics 3 Journal of Elasticity 3 SIAM Journal on Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 Journal of Nonlinear Science 3 Calculus of Variations and Partial Differential Equations 3 Advances in Computational Mathematics 3 Nonlinear Analysis. Real World Applications 3 SIAM Journal on Applied Dynamical Systems 3 Advances in Difference Equations 3 Oberwolfach Reports 3 Nonlinear Analysis. Theory, Methods & Applications 2 Communications in Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Theoretical and Computational Fluid Dynamics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Mathematics and Computers in Simulation 2 Meccanica 2 Applied Mathematics and Mechanics. (English Edition) 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Acta Mathematicae Applicatae Sinica. English Series 2 Computational Mechanics 2 Applied Mathematics Letters 2 European Journal of Applied Mathematics 2 Applications of Mathematics 2 Applied Mathematical Modelling 2 Communications in Partial Differential Equations 2 International Journal of Computer Mathematics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Review 2 Bulletin of the American Mathematical Society. New Series 2 NoDEA. Nonlinear Differential Equations and Applications 2 Complexity 2 Journal of Difference Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Discrete and Continuous Dynamical Systems. Series B 2 Acta Numerica 2 International Journal of Numerical Analysis and Modeling 2 Journal of Physics A: Mathematical and Theoretical 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Results in Applied Mathematics 1 Acta Mechanica 1 Computer Physics Communications 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Reports on Mathematical Physics 1 Journal of Geometry and Physics 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Optimization 1 Czechoslovak Mathematical Journal ...and 71 more Serials all top 5 Cited in 39 Fields 414 Numerical analysis (65-XX) 314 Partial differential equations (35-XX) 218 Mechanics of deformable solids (74-XX) 129 Statistical mechanics, structure of matter (82-XX) 117 Fluid mechanics (76-XX) 76 Calculus of variations and optimal control; optimization (49-XX) 36 Dynamical systems and ergodic theory (37-XX) 33 Optics, electromagnetic theory (78-XX) 30 Quantum theory (81-XX) 28 Probability theory and stochastic processes (60-XX) 21 Ordinary differential equations (34-XX) 21 Mechanics of particles and systems (70-XX) 19 Operator theory (47-XX) 11 Operations research, mathematical programming (90-XX) 10 Real functions (26-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Biology and other natural sciences (92-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Integral equations (45-XX) 7 Functional analysis (46-XX) 6 Approximations and expansions (41-XX) 6 Computer science (68-XX) 5 Geophysics (86-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Potential theory (31-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Systems theory; control (93-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Relativity and gravitational theory (83-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year