Luskin, Mitchell

Compute Distance To:
 Author ID: luskin.mitchell Published as: Luskin, Mitchell; Luskin, M.
 Documents Indexed: 108 Publications since 1979 5 Contributions as Editor Co-Authors: 70 Co-Authors with 99 Joint Publications 2,450 Co-Co-Authors
all top 5

Co-Authors

 13 single-authored 15 Ortner, Christoph 10 Bělík, Pavel 8 Dobson, Matthew 5 Li, Bo 5 Maier, Matthias Sebastian 5 Margetis, Dionisios 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. 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 Kružík, Martin 1 Le Bris, Claude 1 Lelièvre, Tony 1 Lin, Sanyih 1 Lorence, Leonard J. jun. 1 Lucas, Andrew 1 Ma, Ling 1 Majda, Andrew J. 1 Martin, William R. 1 Mattheakis, M. 1 Pan, Tsorng-Whay 1 Rappaz, Jacques 1 Riordan, James 1 Rybka, Piotr 1 Srolovitz, David J. 1 Voter, Arthur F. 1 Watson, Alexander B. 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 The IMA Volumes in Mathematics and its Applications 4 Archive for Rational Mechanics and Analysis 4 Journal of Mathematical Physics 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 Lectures in Applied Mathematics 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) 40 Statistical mechanics, structure of matter (82-XX) 24 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) 5 General and overarching topics; collections (00-XX) 5 Quantum theory (81-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)

Citations contained in zbMATH Open

91 Publications have been cited 1,086 times in 663 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
2003
On the computation of crystalline microstructure. Zbl 0867.65033
Luskin, Mitchell
1996
On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064
Luskin, Mitchell; Rannacher, Rolf
1982
Atomistic-to-continuum coupling. Zbl 1464.74007
Luskin, Mitchell; Ortner, Christoph
2013
On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062
Luskin, Mitchell; Rannacher, Rolf
1982
The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054
Luskin, Mitchell; Temple, Blake
1982
A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059
Luskin, Mitchell
1979
Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006
Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph
2010
Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006
Dobson, Matthew; Luskin, Mitchell
2008
Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123
Luskin, M.; Ortner, C.; Van Koten, B.
2013
Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081
Klouček, Petr; Li, Bo; Luskin, Mitchell
1996
Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067
Collins, Charles; Kinderlehrer, David; Luskin, Mitchell
1991
Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002
Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard
2007
The computation of the austenitic-martensitic phase transition. Zbl 0991.80502
Collins, Charles; Luskin, Mitchell
1989
Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047
Fabes, Eugene; Luskin, Mitchell; Sell, George R.
1991
An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122
Luskin, Mitchell; Ortner, Christoph
2009
A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045
Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny
2012
An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089
Dobson, Matthew; Luskin, Mitchell
2009
The computation of the dynamics of the martensitic transformation. Zbl 0825.73047
Klouček, P.; Luskin, M.
1994
Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113
Luskin, Mitchell; Ma, Ling
1992
Relaxation methods for liquid crystal problems. Zbl 0685.65058
Lin, San-Yih; Luskin, Mitchell
1989
Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313
Arndt, Marcel; Luskin, Mitchell
2008
An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414
Dobson, Matthew; Luskin, Mitchell
2009
The simply laminated microstructure in martensitic crystals that undergo a cubic-to-orthorhombic phase transformation. Zbl 0942.74056
Bhattacharya, Kaushik; Li, Bo; Luskin, Mitchell
1999
Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004
Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V.
2014
Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026
Van Koten, Brian; Luskin, Mitchell
2011
Approximation theories for inertial manifolds. Zbl 0688.58035
Luskin, Mitchell; Sell, George R.
1989
Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085
Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre
2000
Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009
Dobson, M.; Luskin, M.; Ortner, C.
2010
Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005
Dobson, M.; Luskin, M.; Ortner, C.
2010
Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem. Zbl 0735.65042
Collins, Charles; Luskin, Mitchell
1991
Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014
Rybka, Piotr; Luskin, Mitchell
2005
On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014
Luskin, Mitchell
1981
An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220
Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V.
2014
Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012
Arndt, Marcel; Luskin, Mitchell
2008
The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039
Kružík, Martin; Luskin, Mitchell
2003
Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084
Chipot, Michel; Luskin, Mitchell
1986
Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076
Li, Bo; Luskin, Mitchell
1998
Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066
Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard
2009
Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048
Collins, Charles; Luskin, Mitchell; Riordan, James
1993
Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060
Luskin, Mitchell
1996
Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020
Li, Bo; Luskin, Mitchell
1998
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
1981
A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078
Li, Xingjie Helen; Luskin, Mitchell
2012
Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012
Li, Bo; Luskin, Mitchell
1999
Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107
Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph
2012
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.
2014
Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015
Cohen, Robert; Luskin, Mitchell
1991
Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222
Dobson, M.; Luskin, M.; Ortner, C.
2011
Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020
Bělík, Pavel; Luskin, Mitchell
2003
Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064
Klouček, P.; Luskin, M.
1994
Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042
Bělík, Pavel; Luskin, Mitchell
2000
A computational and theoretical investigation of the accuracy of quasicontinuum methods. Zbl 1245.74102
Van Koten, Brian; Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph
2012
Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037
Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell
2017
Approximation of crystalline defects at finite temperature. Zbl 1378.82046
Shapeev, Alexander V.; Luskin, Mitchell
2017
Electronic density of states for incommensurate layers. Zbl 1365.81164
Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph
2017
On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047
Bělík, Pavel; Brule, Timothy; Luskin, Mitchell
2001
Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053
Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell
1988
A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013
Bělík, Pavel; Luskin, Mitchell
2002
A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059
Bělík, Pavel; Luskin, Mitchell
2002
Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099
Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell
2017
Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085
Dobson, Matthew; Luskin, Mitchell
2008
Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022
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
2016
Parallel solution of partial differential equations. Proceedings of a workshop, Univ. of Minnesota, Minneapolis, MN, USA, June 9–13, 1997. Zbl 0938.00013
2000
A finite element method for first-order hyperbolic systems. Zbl 0447.65064
Luskin, Mitchell
1980
Numerical analysis of parallel replica dynamics. Zbl 1298.65016
Simpson, Gideon; Luskin, Mitchell
2013
Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044
Kheshgi, Haroon; Luskin, Mitchell
1985
On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006
Margetis, Dionisios; Luskin, Mitchell
2016
The $$\Gamma$$-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013
Belík, Pavel; Luskin, Mitchell
2007
Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328
Luskin, Mitchell; Zhang, Tianyu
2007
Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061
Luskin, M.
1991
Computational modeling of microstructure. Zbl 1025.49014
Luskin, Mitchell
2002
An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086
Luskin, Mitchell
1979
Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019
Luskin, Mitchell; Pan, Tsorng-Whay
1992
A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046
Bělík, Pavel; Luskin, Mitchell
2004
Computational modeling of softening in a structural phase transformation. Zbl 1108.74045
Bělík, Pavel; Luskin, Mitchell
2005
Convergence of a finite element method for the approximation of normal modes of the oceans. Zbl 0431.65066
Luskin, Mitchell
1979
Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018
Song, Jung Heon; Maier, Matthias; Luskin, Mitchell
2019
Incommensurate heterostructures in momentum space. Zbl 1434.82101
Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph
2018
On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037
Kheshgi, Haroon; Luskin, Mitchell
1983
On the classification of some model equations for viscoelasticity. Zbl 0559.76011
Luskin, Mitchell
1984
Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004
Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F.
2015
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
2017
A finite element model for martensitic thin films. Zbl 1168.65308
Bělík, Pavel; Luskin, Mitchell
2006
On the stability of microstructure for general martensitic transformations. Zbl 1049.74737
Luskin, M.
2000
The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063
Luskin, Mitchell; Temple, Blake
1982
Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075
Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V.
2014
On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009
Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell
2017
Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042
Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell
2018
Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009
Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D.
2019
Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets. Zbl 1441.78018
Song, Jung Heon; Maier, Matthias; Luskin, Mitchell
2019
Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect. Zbl 1472.78009
Maier, M.; Mattheakis, M.; Kaxiras, E.; Luskin, M.; Margetis, D.
2019
Incommensurate heterostructures in momentum space. Zbl 1434.82101
Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph
2018
Generation of surface plasmon-polaritons by edge effects. Zbl 1383.78042
Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell
2018
Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation. Zbl 1375.78037
Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell
2017
Approximation of crystalline defects at finite temperature. Zbl 1378.82046
Shapeev, Alexander V.; Luskin, Mitchell
2017
Electronic density of states for incommensurate layers. Zbl 1365.81164
Massatt, Daniel; Luskin, Mitchell; Ortner, Christoph
2017
Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures. Zbl 1371.82099
Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell
2017
Analysis of rippling in incommensurate one-dimensional coupled chains. Zbl 1383.74022
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
2017
On the Wiener-Hopf method for surface plasmons: diffraction from semiinfinite metamaterial sheet. Zbl 1386.78009
Margetis, Dionisios; Maier, Matthias; Luskin, Mitchell
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
2016
On solutions of Maxwell’s equations with dipole sources over a thin conducting film. Zbl 1347.78006
Margetis, Dionisios; Luskin, Mitchell
2016
Analysis of transition state theory rates upon spatial coarse-graining. Zbl 1329.82004
Binder, Andrew; Luskin, Mitchell; Perez, Danny; Voter, Arthur F.
2015
Theory-based benchmarking of the blended force-based quasicontinuum method. Zbl 1295.74004
Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph; Shapeev, Alexander V.
2014
An optimization-based atomistic-to-continuum coupling method. Zbl 1306.65220
Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell; Shapeev, Alexander V.
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.
2014
Development of an optimization-based atomistic-to-continuum coupling method. Zbl 1446.74075
Olson, Derek; Bochev, Pavel; Luskin, Mitchell; Shapeev, Alexander V.
2014
Atomistic-to-continuum coupling. Zbl 1464.74007
Luskin, Mitchell; Ortner, Christoph
2013
Formulation and optimization of the energy-based blended quasicontinuum method. Zbl 1297.74123
Luskin, M.; Ortner, C.; Van Koten, B.
2013
Numerical analysis of parallel replica dynamics. Zbl 1298.65016
Simpson, Gideon; Luskin, Mitchell
2013
A mathematical formalization of the parallel replica dynamics. Zbl 1243.82045
Le Bris, Claude; Lelièvre, Tony; Luskin, Mitchell; Perez, Danny
2012
A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction. Zbl 1241.82078
Li, Xingjie Helen; Luskin, Mitchell
2012
Positive definiteness of the blended force-based quasicontinuum method. Zbl 1257.82107
Li, Xingjie Helen; Luskin, Mitchell; Ortner, Christoph
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
2012
Analysis of energy-based blended quasi-continuum approximations. Zbl 1241.82026
Van Koten, Brian; Luskin, Mitchell
2011
Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem. Zbl 1230.74222
Dobson, M.; Luskin, M.; Ortner, C.
2011
Stability, instability, and error of the force-based quasicontinuum approximation. Zbl 1268.74006
Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph
2010
Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Zbl 1225.82009
Dobson, M.; Luskin, M.; Ortner, C.
2010
Accuracy of quasicontinuum approximations near instabilities. Zbl 1200.74005
Dobson, M.; Luskin, M.; Ortner, C.
2010
An analysis of node-based cluster summation rules in the quasicontinuum method. Zbl 1196.82122
Luskin, Mitchell; Ortner, Christoph
2009
An optimal order error analysis of the one-dimensional quasicontinuum approximation. Zbl 1203.82089
Dobson, Matthew; Luskin, Mitchell
2009
An analysis of the effect of ghost force oscillation on quasicontinuum error. Zbl 1165.81414
Dobson, Matthew; Luskin, Mitchell
2009
Non-ergodicity of Nosé-Hoover dynamics. Zbl 1173.37066
Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard
2009
Analysis of a force-based quasicontinuum approximation. Zbl 1140.74006
Dobson, Matthew; Luskin, Mitchell
2008
Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1160.82313
Arndt, Marcel; Luskin, Mitchell
2008
Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Zbl 1194.74012
Arndt, Marcel; Luskin, Mitchell
2008
Iterative solution of the quasicontinuum equilibrium equations with continuation. Zbl 1203.65085
Dobson, Matthew; Luskin, Mitchell
2008
Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Zbl 1122.82002
Legoll, Frédéric; Luskin, Mitchell; Moeckel, Richard
2007
The $$\Gamma$$-convergence of a sharp interface thin film model with nonconvex elastic energy. Zbl 1109.49013
Belík, Pavel; Luskin, Mitchell
2007
Numerical analysis of a model for ferromagnetic shape memory thin films. Zbl 1173.74328
Luskin, Mitchell; Zhang, Tianyu
2007
A finite element model for martensitic thin films. Zbl 1168.65308
Bělík, Pavel; Luskin, Mitchell
2006
Existence of energy minimizers for magnetostrictive materials. Zbl 1086.49014
Rybka, Piotr; Luskin, Mitchell
2005
Computational modeling of softening in a structural phase transformation. Zbl 1108.74045
Bělík, Pavel; Luskin, Mitchell
2005
A computational model for martensitic thin films with compositional fluctuation. Zbl 1101.74046
Bělík, Pavel; Luskin, Mitchell
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
2003
The computation of martensitic microstructure with piecewise laminates. Zbl 1039.74039
Kružík, Martin; Luskin, Mitchell
2003
Approximation by piecewise constant functions in a BV metric. Zbl 1045.49020
Bělík, Pavel; Luskin, Mitchell
2003
A total-variation surface energy model for thin films of martensitic crystals. Zbl 1014.49013
Bělík, Pavel; Luskin, Mitchell
2002
A computational model for the indentation and phase transformation of a martensitic thin film. Zbl 1004.74059
Bělík, Pavel; Luskin, Mitchell
2002
Computational modeling of microstructure. Zbl 1025.49014
Luskin, Mitchell
2002
On the numerical modeling of deformations of pressurized martensitic thin films. Zbl 1062.74047
Bělík, Pavel; Brule, Timothy; Luskin, Mitchell
2001
Post-processing of Galerkin methods for hyperbolic problems. Zbl 0946.65085
Cockburn, Bernardo; Luskin, Mitchell; Shu, Chi-Wang; Süli, Endre
2000
Stability of microstructure for tetragonal to monoclinic martensitic transformations. Zbl 0981.74042
Bělík, Pavel; Luskin, Mitchell
2000
Parallel solution of partial differential equations. Proceedings of a workshop, Univ. of Minnesota, Minneapolis, MN, USA, June 9–13, 1997. Zbl 0938.00013
2000
On the stability of microstructure for general martensitic transformations. Zbl 1049.74737
Luskin, M.
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
1999
Approximation of a martensitic laminate with varying fractions. Zbl 0928.74012
Li, Bo; Luskin, Mitchell
1999
Nonconforming finite element approximation of crystalline microstructure. Zbl 0901.73076
Li, Bo; Luskin, Mitchell
1998
Finite element analysis of microstructure for the cubic to tetragonal transformation. Zbl 0919.49020
Li, Bo; Luskin, Mitchell
1998
On the computation of crystalline microstructure. Zbl 0867.65033
Luskin, Mitchell
1996
Analysis of a class of nonconforming finite elements for crystalline microstructures. Zbl 0903.65081
Klouček, Petr; Li, Bo; Luskin, Mitchell
1996
Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Zbl 0874.73060
Luskin, Mitchell
1996
The computation of the dynamics of the martensitic transformation. Zbl 0825.73047
Klouček, P.; Luskin, M.
1994
Computational modeling of the martensitic transformation with surface energy. Zbl 0813.73064
Klouček, P.; Luskin, M.
1994
Computational results for a two-dimensional model of crystalline microstructure. Zbl 0797.73048
Collins, Charles; Luskin, Mitchell; Riordan, James
1993
Analysis of the finite element approximation of microstructure in micromagnetics. Zbl 0760.65113
Luskin, Mitchell; Ma, Ling
1992
Non-planar shear flows for non-aligning nematic liquid crystals. Zbl 0747.76019
Luskin, Mitchell; Pan, Tsorng-Whay
1992
Numerical approximation of the solution of a variational problem with a double well potential. Zbl 0725.65067
Collins, Charles; Kinderlehrer, David; Luskin, Mitchell
1991
Construction of inertial manifolds by elliptic regularization. Zbl 0728.34047
Fabes, Eugene; Luskin, Mitchell; Sell, George R.
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
1991
Field-induced instabilities in nematic liquid crystals. Zbl 0727.76015
Cohen, Robert; Luskin, Mitchell
1991
Numerical analysis of microstructure for crystals with nonconvex energy density. Zbl 0784.65061
Luskin, M.
1991
The computation of the austenitic-martensitic phase transition. Zbl 0991.80502
Collins, Charles; Luskin, Mitchell
1989
Relaxation methods for liquid crystal problems. Zbl 0685.65058
Lin, San-Yih; Luskin, Mitchell
1989
Approximation theories for inertial manifolds. Zbl 0688.58035
Luskin, Mitchell; Sell, George R.
1989
Remarks about the mathematical theory of liquid crystals. Zbl 0696.49053
Hardt, Robert; Kinderlehrer, David; Luskin, Mitchell
1988
Existence and uniqueness of solutions to the compressible Reynolds lubrication equation. Zbl 0645.76084
Chipot, Michel; Luskin, Mitchell
1986
Analysis of the finite element variable penalty method for Stokes equations. Zbl 0591.76044
Kheshgi, Haroon; Luskin, Mitchell
1985
On the classification of some model equations for viscoelasticity. Zbl 0559.76011
Luskin, Mitchell
1984
On the variable sign penalty approximation of the Navier-Stokes equation. Zbl 0515.76037
Kheshgi, Haroon; Luskin, Mitchell
1983
On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064
Luskin, Mitchell; Rannacher, Rolf
1982
On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062
Luskin, Mitchell; Rannacher, Rolf
1982
The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0489.35054
Luskin, Mitchell; Temple, Blake
1982
The existence of a global weak solution to the nonlinear waterhammer problem. Zbl 0479.35063
Luskin, Mitchell; Temple, Blake
1982
On the existence of global smooth solutions for a model equation for fluid flow in a pipe. Zbl 0485.76014
Luskin, Mitchell
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
1981
A finite element method for first-order hyperbolic systems. Zbl 0447.65064
Luskin, Mitchell
1980
A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. Zbl 0405.65059
Luskin, Mitchell
1979
An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions. Zbl 0399.65086
Luskin, Mitchell
1979
Convergence of a finite element method for the approximation of normal modes of the oceans. Zbl 0431.65066
Luskin, Mitchell
1979
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Cited by 866 Authors

 41 Luskin, Mitchell 32 Ortner, Christoph 22 Ryan, Jennifer K. 15 Carstensen, Carsten 12 Kružík, Martin 11 Wang, Junjun 9 Lelièvre, Tony 9 Roubíček, Tomáš 9 Shapeev, Alexander V. 9 Shi, Dongyang 9 Shi, Zhongci 9 Sinha, Rajen Kumar 8 Bartels, Sören 8 Klouček, Petr 8 Li, Zhiping 7 Basaran, Osman A. 7 Chen, Huajie 7 Ming, Pingbing 7 Nochetto, Ricardo Horacio 7 Zhang, Lei 6 Bělík, Pavel 6 Bochev, Pavel B. 6 Dobson, Matthew 6 Leimkuhler, Benedict J. 6 Li, Xiaozhou 6 Lin, Ping 6 Pedregal, Pablo 6 Plecháč, Petr 6 Sell, George Roger 6 Stefanelli, Ulisse 6 Titi, Edriss Saleh 6 Walker, Shawn W. 5 Chipot, Michel 5 Cockburn, Bernardo 5 Hong, John Meng-Kai 5 Li, Xiantao 5 Liao, Mingjie 5 Mao, Shipeng 5 Nectoux, Boris 5 Shu, Chi-Wang 5 Zhang, Zhimin 4 Azaïez, Mejdi 4 Baccouch, Mahboub 4 Conti, Sergio 4 Jolly, Michael S. 4 Kinderlehrer, David 4 Le Peutrec, Dorian 4 Legoll, Frédéric 4 Li, Xingjie Helen 4 Lu, Jianfeng 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 Wang, Hao 4 Yang, Qingcheng 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 Braun, Julian 3 Butler, Leo T. 3 Cancès, Eric 3 Cazeaux, Paul 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 Hackl, Klaus 3 Huang, Feimin 3 Jacobs, Gustaaf B. 3 Jai, Mohammed 3 Jallepalli, Ashok 3 Ji, Liangyue 3 Jin, Bangti 3 Jones, Don A. 3 Khaliq, Abdul Q. M. 3 Kim, Soojung 3 Kong, Dexing 3 Li, Bo 3 Li, Buyang ...and 766 more Authors
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Cited in 160 Serials

 45 Computer Methods in Applied Mechanics and Engineering 40 Journal of Scientific Computing 31 Mathematics of Computation 25 Journal of Computational Physics 22 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 Multiscale Modeling & Simulation 17 Applied Numerical Mathematics 14 Journal of Mathematical Analysis and Applications 14 Journal of Differential Equations 14 SIAM Journal on Numerical Analysis 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 11 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 11 SIAM Journal on Scientific Computing 10 Computers & Mathematics with Applications 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 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 in Computational 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 Journal of Mathematical Physics 5 Calcolo 5 International Journal for Numerical Methods in Engineering 5 Mathematical and Computer Modelling 4 Computational and Applied Mathematics 4 Science China. Mathematics 4 Communications on Applied Mathematics and Computation 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 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 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 Advances in Difference Equations 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 Chaos, Solitons and Fractals 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 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire ...and 60 more Serials
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Cited in 38 Fields

 359 Numerical analysis (65-XX) 269 Partial differential equations (35-XX) 193 Mechanics of deformable solids (74-XX) 110 Fluid mechanics (76-XX) 103 Statistical mechanics, structure of matter (82-XX) 72 Calculus of variations and optimal control; optimization (49-XX) 29 Dynamical systems and ergodic theory (37-XX) 23 Quantum theory (81-XX) 22 Probability theory and stochastic processes (60-XX) 22 Optics, electromagnetic theory (78-XX) 20 Ordinary differential equations (34-XX) 20 Mechanics of particles and systems (70-XX) 16 Operator theory (47-XX) 11 Operations research, mathematical programming (90-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Biology and other natural sciences (92-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) 5 Approximations and expansions (41-XX) 4 Geophysics (86-XX) 3 History and biography (01-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Computer science (68-XX) 3 Systems theory; control (93-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-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 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)