Edit Profile (opens in new tab) Luskin, Mitchell Compute Distance To: Compute Author ID: luskin.mitchell Published as: Luskin, Mitchell; Luskin, M. Documents Indexed: 110 Publications since 1979 5 Contributions as Editor Co-Authors: 74 Co-Authors with 101 Joint Publications 2,574 Co-Co-Authors all top 5 Co-Authors 13 single-authored 15 Ortner, Christoph 10 Bělík, Pavel 8 Dobson, Matthew 6 Maier, Matthias Sebastian 6 Margetis, Dionisios 5 Li, Bo 5 Shapeev, Alexander V. 4 Collins, Charles R. 4 Li, Xingjie Helen 4 Massatt, Daniel 4 Vankoten, Brian 3 Bochev, Pavel B. 3 Cazeaux, Paul 3 Chipot, Michel 3 Kheshgi, Haroon S. 3 Kinderlehrer, David 3 Klouček, Petr 3 Olson, Derek 3 Perez, Danny 3 Temple, Blake 2 Arndt, Marcel 2 Binder, Andrew J. 2 Cockburn, Bernardo 2 Descloux, Jean 2 Legoll, Frédéric 2 Moeckel, Richard 2 Rannacher, Rolf 2 Sell, George Roger 2 Shu, Chi-Wang 2 Simpson, Gideon 2 Song, Jung Heon 2 Süli, Endre E. 2 Tadmor, Ellad B. 2 Watson, Alexander B. 1 Bal, Guillaume 1 Bern, Marshall W. 1 Bhattacharya, Kaushik 1 Bjørstad, Petter Erling 1 Brule, Timothy 1 Cancès, Eric 1 Carr, Stephen 1 Efendiev, Yalchin R. 1 Engquist, Bjorn E. 1 Ericksen, Jerald Laverne 1 Etter, Simon 1 Fabes, Eugene B. 1 Flaherty, Joseph E. 1 Golub, Gene Howard 1 Greenbaum, Anne 1 Hardt, Robert M. 1 James, Richard D. 1 Kaxiras, Efthimios 1 Kim, Woo Kyun 1 Kong, Tianyu 1 Kružík, Martin 1 Le Bris, Claude 1 Lelièvre, Tony 1 Lin, Sanyih 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 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 13 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 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 Studies in Applied Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 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 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 57 Numerical analysis (65-XX) 47 Mechanics of deformable solids (74-XX) 42 Statistical mechanics, structure of matter (82-XX) 25 Partial differential equations (35-XX) 18 Fluid mechanics (76-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 11 Mechanics of particles and systems (70-XX) 8 Optics, electromagnetic theory (78-XX) 6 Quantum theory (81-XX) 5 General and overarching topics; collections (00-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 93 Publications have been cited 1,131 times in 691 Documents Cited by ▼ Year ▼ Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 84 2003 On the computation of crystalline microstructure. Zbl 0867.65033Luskin, Mitchell 64 1996 On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064Luskin, Mitchell; Rannacher, Rolf 57 1982 Atomistic-to-continuum coupling. Zbl 1464.74007Luskin, Mitchell; Ortner, Christoph 42 2013 On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062Luskin, Mitchell; Rannacher, Rolf 38 1982 A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059Luskin, Mitchell 31 1979 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054Luskin, Mitchell; Temple, Blake 30 1982 Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph 26 2010 Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006Dobson, Matthew; Luskin, Mitchell 24 2008 Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067Collins, Charles; Kinderlehrer, David; Luskin, Mitchell 22 1991 Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123Luskin, M.; Ortner, C.; Van Koten, B. 22 2013 A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny 21 2012 Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081Klouček, Petr; Li, Bo; Luskin, Mitchell 21 1996 Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 21 2007 Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047Fabes, Eugene; Luskin, Mitchell; Sell, George R. 20 1991 The computation of the austenitic-martensitic phase transition. Zbl 0991.80502Collins, Charles; Luskin, Mitchell 20 1989 An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122Luskin, Mitchell; Ortner, Christoph 19 2009 Relaxation methods for liquid crystal problems. Zbl 0685.65058Lin, San-Yih; Luskin, Mitchell 18 1989 The computation of the dynamics of the martensitic transformation. Zbl 0825.73047Klouček, P.; Luskin, M. 18 1994 An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089Dobson, Matthew; Luskin, Mitchell 18 2009 Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113Luskin, Mitchell; Ma, Ling 17 1992 Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313Arndt, Marcel; Luskin, Mitchell 17 2008 An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414Dobson, Matthew; Luskin, Mitchell 16 2009 The simply laminated microstructure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation. Zbl 0942.74056Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell 16 1999 Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V. 16 2014 An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V. 16 2014 Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009Dobson, M.; Luskin, M.; Ortner, C. 16 2010 Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 15 2000 Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026Van Koten, Brian; Luskin, Mitchell 15 2011 Approximation theories for inertial manifolds. Zbl 0688.58035Luskin, Mitchell; Sell, George R. 15 1989 Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005Dobson, M.; Luskin, M.; Ortner, C. 15 2010 Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem. Zbl 0735.65042Collins, Charles; Luskin, Mitchell 14 1991 Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014Rybka, Piotr; Luskin, Mitchell 14 2005 On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014Luskin, Mitchell 14 1981 Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012Arndt, Marcel; Luskin, Mitchell 14 2008 The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039Kružík, Martin; Luskin, Mitchell 13 2003 Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084Chipot, Michel; Luskin, Mitchell 13 1986 Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 12 2009 Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048Collins, Charles; Luskin, Mitchell; Riordan, James 12 1993 Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076Li, Bo; Luskin, Mitchell 12 1998 Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060Luskin, Mitchell 11 1996 Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020Li, Bo; Luskin, Mitchell 10 1998 Approximation of the spectrum of closed operators: The determination of normal modes of a rotating basin. Zbl 0458.65084Descloux, Jean; Luskin, Mitchell; Rappaz, Jacques 9 1981 Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 8 2012 A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078Li, Xingjie Helen; Luskin, Mitchell 8 2012 Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 8 2017 Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012Li, Bo; Luskin, Mitchell 8 1999 Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015Cohen, Robert; Luskin, Mitchell 7 1991 Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics. Zbl 1303.74007Kim, W. K.; Luskin, M.; Perez, D.; Voter, A. F.; Tadmor, E. B. 7 2014 Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042Bělík, Pavel; Luskin, Mitchell 6 2000 Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020Bělík, Pavel; Luskin, Mitchell 6 2003 Approximation of crystalline defects at finite temperature. Zbl 1378.82046Shapeev, Alexander V.; Luskin, Mitchell 6 2017 Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222Dobson, M.; Luskin, M.; Ortner, C. 6 2011 A computational and theoretical investigation of the accuracy of quasicontinuum methods. Zbl 1245.74102Van Koten, Brian; Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 6 2012 Electronic density of states for incommensurate layers. Zbl 1365.81164Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 6 2017 Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell 6 2017 Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064Klouček, P.; Luskin, M. 6 1994 A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013Bělík, Pavel; Luskin, Mitchell 6 2002 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 Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell 5 1988 On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047Bělík, Pavel; Brule, Timothy; Luskin, Mitchell 5 2001 Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085Dobson, Matthew; Luskin, Mitchell 5 2008 A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059Bělík, Pavel; Luskin, Mitchell 5 2002 On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006Margetis, Dionisios; Luskin, Mitchell 4 2016 A finite element method for first-order hyperbolic systems. Zbl 0447.65064Luskin, Mitchell 4 1980 Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. Zbl 1353.82022Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; Luskin, Mitchell 4 2016 Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022Cazeaux, Paul; Luskin, Mitchell; Tadmor, Ellad B. 4 2017 Numerical analysis of parallel replica dynamics. Zbl 1298.65016Simpson, Gideon; Luskin, Mitchell 4 2013 Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018Song, Jung Heon; Maier, Matthias; Luskin, Mitchell 4 2019 Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044Kheshgi, Haroon; Luskin, Mitchell 3 1985 Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328Luskin, Mitchell; Zhang, Tianyu 3 2007 Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061Luskin, M. 3 1991 The \(\Gamma\)-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013Belík, Pavel; Luskin, Mitchell 3 2007 Computational modeling of microstructure. Zbl 1025.49014Luskin, Mitchell 3 2002 An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086Luskin, Mitchell 3 1979 Incommensurate heterostructures in momentum space. Zbl 1434.82101Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph 3 2018 Computational modeling of softening in a structural phase transformation. Zbl 1108.74045Bělík, Pavel; Luskin, Mitchell 2 2005 Convergence of a finite element method for the approximation of normal modes of the oceans. Zbl 0431.65066Luskin, Mitchell 2 1979 A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046Bělík, Pavel; Luskin, Mitchell 2 2004 Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019Luskin, Mitchell; Pan, Tsorng-Whay 2 1992 Existence of the first magic angle for the chiral model of bilayer graphene. Zbl 1506.82045Watson, Alexander B.; Luskin, Mitchell 2 2021 Energy minimization of two dimensional incommensurate heterostructures. Zbl 1433.74051Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel 2 2020 A finite element model for martensitic thin films. Zbl 1168.65308Bělík, Pavel; Luskin, Mitchell 1 2006 Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F. 1 2015 Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V. 1 2014 On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell 1 2017 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063Luskin, Mitchell; Temple, Blake 1 1982 On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037Kheshgi, Haroon; Luskin, Mitchell 1 1983 On the classification of some model equations for viscoelasticity. Zbl 0559.76011Luskin, Mitchell 1 1984 Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1D. Zbl 1362.74009Binder, Andrew J.; Luskin, Mitchell; Ortner, Christoph 1 2017 Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 1 2018 Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D. 1 2019 On the stability of microstructure for general martensitic transformations. Zbl 1049.74737Luskin, M. 1 2000 Existence of the first magic angle for the chiral model of bilayer graphene. Zbl 1506.82045Watson, Alexander B.; Luskin, Mitchell 2 2021 Energy minimization of two dimensional incommensurate heterostructures. Zbl 1433.74051Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel 2 2020 Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018Song, Jung Heon; Maier, Matthias; Luskin, Mitchell 4 2019 Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D. 1 2019 Incommensurate heterostructures in momentum space. Zbl 1434.82101Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph 3 2018 Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 1 2018 Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell 8 2017 Approximation of crystalline defects at finite temperature. Zbl 1378.82046Shapeev, Alexander V.; Luskin, Mitchell 6 2017 Electronic density of states for incommensurate layers. Zbl 1365.81164Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph 6 2017 Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell 6 2017 Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022Cazeaux, Paul; Luskin, Mitchell; Tadmor, Ellad B. 4 2017 On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell 1 2017 Analysis of a predictor-corrector method for computationally efficient modeling of surface effects in 1D. Zbl 1362.74009Binder, Andrew J.; Luskin, Mitchell; Ortner, Christoph 1 2017 On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006Margetis, Dionisios; Luskin, Mitchell 4 2016 Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. Zbl 1353.82022Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; Luskin, Mitchell 4 2016 Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F. 1 2015 Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V. 16 2014 An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V. 16 2014 Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics. Zbl 1303.74007Kim, W. K.; Luskin, M.; Perez, D.; Voter, A. F.; Tadmor, E. B. 7 2014 Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V. 1 2014 Atomistic-to-continuum coupling. Zbl 1464.74007Luskin, Mitchell; Ortner, Christoph 42 2013 Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123Luskin, M.; Ortner, C.; Van Koten, B. 22 2013 Numerical analysis of parallel replica dynamics. Zbl 1298.65016Simpson, Gideon; Luskin, Mitchell 4 2013 A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny 21 2012 Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 8 2012 A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078Li, Xingjie Helen; Luskin, Mitchell 8 2012 A computational and theoretical investigation of the accuracy of quasicontinuum methods. Zbl 1245.74102Van Koten, Brian; Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph 6 2012 Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026Van Koten, Brian; Luskin, Mitchell 15 2011 Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222Dobson, M.; Luskin, M.; Ortner, C. 6 2011 Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph 26 2010 Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009Dobson, M.; Luskin, M.; Ortner, C. 16 2010 Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005Dobson, M.; Luskin, M.; Ortner, C. 15 2010 An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122Luskin, Mitchell; Ortner, Christoph 19 2009 An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089Dobson, Matthew; Luskin, Mitchell 18 2009 An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414Dobson, Matthew; Luskin, Mitchell 16 2009 Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 12 2009 Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006Dobson, Matthew; Luskin, Mitchell 24 2008 Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313Arndt, Marcel; Luskin, Mitchell 17 2008 Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012Arndt, Marcel; Luskin, Mitchell 14 2008 Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085Dobson, Matthew; Luskin, Mitchell 5 2008 Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard 21 2007 Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328Luskin, Mitchell; Zhang, Tianyu 3 2007 The \(\Gamma\)-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013Belík, Pavel; Luskin, Mitchell 3 2007 A finite element model for martensitic thin films. Zbl 1168.65308Bělík, Pavel; Luskin, Mitchell 1 2006 Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014Rybka, Piotr; Luskin, Mitchell 14 2005 Computational modeling of softening in a structural phase transformation. Zbl 1108.74045Bělík, Pavel; Luskin, Mitchell 2 2005 A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046Bělík, Pavel; Luskin, Mitchell 2 2004 Enhanced accuracy by post-processing for finite element methods for hyperbolic equations. Zbl 1015.65049Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 84 2003 The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039Kružík, Martin; Luskin, Mitchell 13 2003 Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020Bělík, Pavel; Luskin, Mitchell 6 2003 A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013Bělík, Pavel; Luskin, Mitchell 6 2002 A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059Bělík, Pavel; Luskin, Mitchell 5 2002 Computational modeling of microstructure. Zbl 1025.49014Luskin, Mitchell 3 2002 On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047Bělík, Pavel; Brule, Timothy; Luskin, Mitchell 5 2001 Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre 15 2000 Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042Bělík, 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 1049.74737Luskin, M. 1 2000 The simply laminated microstructure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation. Zbl 0942.74056Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell 16 1999 Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012Li, Bo; Luskin, Mitchell 8 1999 Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076Li, Bo; Luskin, Mitchell 12 1998 Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020Li, Bo; Luskin, Mitchell 10 1998 On the computation of crystalline microstructure. Zbl 0867.65033Luskin, Mitchell 64 1996 Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081Klouček, Petr; Li, Bo; Luskin, Mitchell 21 1996 Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060Luskin, Mitchell 11 1996 The computation of the dynamics of the martensitic transformation. Zbl 0825.73047Klouček, P.; Luskin, M. 18 1994 Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064Klouček, P.; Luskin, M. 6 1994 Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048Collins, Charles; Luskin, Mitchell; Riordan, James 12 1993 Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113Luskin, Mitchell; Ma, Ling 17 1992 Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019Luskin, Mitchell; Pan, Tsorng-Whay 2 1992 Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067Collins, Charles; Kinderlehrer, David; Luskin, Mitchell 22 1991 Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047Fabes, 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 0735.65042Collins, Charles; Luskin, Mitchell 14 1991 Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015Cohen, Robert; Luskin, Mitchell 7 1991 Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061Luskin, M. 3 1991 The computation of the austenitic-martensitic phase transition. Zbl 0991.80502Collins, Charles; Luskin, Mitchell 20 1989 Relaxation methods for liquid crystal problems. Zbl 0685.65058Lin, San-Yih; Luskin, Mitchell 18 1989 Approximation theories for inertial manifolds. Zbl 0688.58035Luskin, Mitchell; Sell, George R. 15 1989 Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell 5 1988 Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084Chipot, Michel; Luskin, Mitchell 13 1986 Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044Kheshgi, Haroon; Luskin, Mitchell 3 1985 On the classification of some model equations for viscoelasticity. Zbl 0559.76011Luskin, Mitchell 1 1984 On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037Kheshgi, Haroon; Luskin, Mitchell 1 1983 On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064Luskin, Mitchell; Rannacher, Rolf 57 1982 On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062Luskin, Mitchell; Rannacher, Rolf 38 1982 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054Luskin, Mitchell; Temple, Blake 30 1982 The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063Luskin, Mitchell; Temple, Blake 1 1982 On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014Luskin, Mitchell 14 1981 Approximation of the spectrum of closed operators: The determination of normal modes of a rotating basin. Zbl 0458.65084Descloux, Jean; Luskin, Mitchell; Rappaz, Jacques 9 1981 A finite element method for first-order hyperbolic systems. Zbl 0447.65064Luskin, Mitchell 4 1980 A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059Luskin, Mitchell 31 1979 An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086Luskin, Mitchell 3 1979 Convergence of a finite element method for the approximation of normal modes of the oceans. Zbl 0431.65066Luskin, Mitchell 2 1979 all cited Publications top 5 cited Publications all top 5 Cited by 905 Authors 43 Luskin, Mitchell 33 Ortner, Christoph 25 Ryan, Jennifer K. 15 Carstensen, Carsten 13 Kirby, Robert M. II 12 Kružík, Martin 11 Wang, Junjun 9 Bartels, Sören 9 Lelièvre, Tony 9 Roubíček, Tomáš 9 Shapeev, Alexander V. 9 Shi, Dongyang 9 Shi, Zhongci 9 Sinha, Rajen Kumar 8 Klouček, Petr 8 Li, Zhiping 8 Zhang, Lei 7 Basaran, Osman A. 7 Chen, Huajie 7 Li, Xiaozhou 7 Ming, Pingbing 7 Nochetto, Ricardo Horacio 6 Bělík, Pavel 6 Bochev, Pavel B. 6 Dobson, Matthew 6 Leimkuhler, Benedict J. 6 Lin, Ping 6 Pedregal, Pablo 6 Plecháč, Petr 6 Sell, George Roger 6 Shu, Chi-Wang 6 Stefanelli, Ulisse 6 Titi, Edriss Saleh 6 Walker, Shawn W. 6 Zhang, Zhimin 5 Chipot, Michel 5 Cockburn, Bernardo 5 Hong, John Meng-Kai 5 Li, Xiantao 5 Liao, Mingjie 5 Mao, Shipeng 5 Nectoux, Boris 5 Wang, Hao 4 Azaïez, Mejdi 4 Baccouch, Mahboub 4 Braun, Julian 4 Conti, Sergio 4 Hackl, Klaus 4 Ji, Liangyue 4 Jolly, Michael Summerfield 4 Kinderlehrer, David 4 Le Peutrec, Dorian 4 Legoll, Frédéric 4 Li, Xingjie Helen 4 Lu, Jianfeng 4 Maier, Matthias Sebastian 4 Margetis, Dionisios 4 Meng, Xiong 4 Miehe, Christian 4 Mirzaee, Hanieh 4 Nakao, Mitsuhiro T. 4 Ortiz, Michael 4 Pan, Ronghua 4 Praetorius, Dirk 4 Prohl, Andreas 4 Shao, Zhiqiang 4 Theil, Florian 4 To, Albert C. 4 Vuik, Cornelis 4 Xu, Yan 4 Yang, Qingcheng 4 Yang, Xiaozhong 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 Butler, Leo T. 3 Cancès, Eric 3 Cang, Shijian 3 Cazeaux, Paul 3 Chen, Zengqiang 3 Chou, Shih-Wei 3 Ciuperca, Ionel Sorin 3 Corli, Andrea 3 D’Elia, Marta 3 Descloux, Jean 3 Deville, Michel O. 3 Dolzmann, Georg 3 Dumbser, Michael 3 Ghidaglia, Jean-Michel 3 Gruber, Ralf 3 Hodapp, Max 3 Huang, Feimin 3 Hudson, Thomas 3 Jacobs, Gustaaf B. 3 Jai, Mohammed ...and 805 more Authors all top 5 Cited in 163 Serials 45 Computer Methods in Applied Mechanics and Engineering 41 Journal of Scientific Computing 31 Mathematics of Computation 29 Journal of Computational Physics 24 Archive for Rational Mechanics and Analysis 21 Journal of the Mechanics and Physics of Solids 18 Journal of Computational and Applied Mathematics 18 Numerische Mathematik 18 Applied Numerical Mathematics 18 Multiscale Modeling & Simulation 15 SIAM Journal on Numerical Analysis 14 Journal of Mathematical Analysis and Applications 14 Journal of Differential Equations 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 12 Computers & Mathematics with Applications 12 SIAM Journal on Scientific Computing 11 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Journal of Statistical Physics 8 Applied Mathematics and Computation 8 Numerical Functional Analysis and Optimization 8 Continuum Mechanics and Thermodynamics 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 RAIRO. Modélisation Mathématique et Analyse Numérique 7 Numerical Methods for Partial Differential Equations 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 Physica D 6 SIAM Journal on Mathematical Analysis 6 Physics of Fluids 5 Applicable Analysis 5 Calcolo 5 International Journal for Numerical Methods in Engineering 5 Mathematical and Computer Modelling 5 Science China. Mathematics 4 Computational and Applied Mathematics 3 Chaos, Solitons and Fractals 3 Computing 3 SIAM Journal on Control and Optimization 3 Science in China. Series A 3 SIAM Journal on Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 Journal of Nonlinear Science 3 Advances in Computational Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Nonlinear Analysis. Real World Applications 3 SIAM Journal on Applied Dynamical Systems 3 Advances in Difference Equations 3 GAMM-Mitteilungen 3 Nonlinear Analysis. Theory, Methods & Applications 2 Mathematical Methods in the Applied Sciences 2 Theoretical and Computational Fluid Dynamics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 BIT 2 Mathematics and Computers in Simulation 2 Meccanica 2 Applied Mathematics and Mechanics. (English Edition) 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 Calculus of Variations and Partial Differential Equations 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 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Results in Applied Mathematics 1 Acta Mechanica 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Reports on Mathematical Physics 1 Journal of Geometry and Physics 1 Applied Mathematics and Optimization 1 Czechoslovak Mathematical Journal 1 Journal of Functional Analysis 1 Journal of Soviet Mathematics 1 Mechanics Research Communications 1 Memoirs of the American Mathematical Society 1 RAIRO. Analyse Numérique 1 Semigroup Forum 1 Transactions of the American Mathematical Society 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 Chinese Annals of Mathematics. Series B ...and 63 more Serials all top 5 Cited in 38 Fields 378 Numerical analysis (65-XX) 291 Partial differential equations (35-XX) 199 Mechanics of deformable solids (74-XX) 111 Fluid mechanics (76-XX) 105 Statistical mechanics, structure of matter (82-XX) 73 Calculus of variations and optimal control; optimization (49-XX) 32 Dynamical systems and ergodic theory (37-XX) 25 Optics, electromagnetic theory (78-XX) 24 Probability theory and stochastic processes (60-XX) 22 Quantum theory (81-XX) 21 Ordinary differential equations (34-XX) 20 Mechanics of particles and systems (70-XX) 17 Operator theory (47-XX) 10 Operations research, mathematical programming (90-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Real functions (26-XX) 7 Integral equations (45-XX) 7 Functional analysis (46-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Biology and other natural sciences (92-XX) 6 Approximations and expansions (41-XX) 5 Geophysics (86-XX) 3 History and biography (01-XX) 3 Computer science (68-XX) 3 Systems theory; control (93-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-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