Michael Neilan

Professor and Graduate Director
Department of Mathematics
University of Pittsburgh
Thackeray 501
lastname "at" pitt "dot" edu

Research interests
Numerical analysis, finite element methods, fully nonlinear problems, mixed methods, discontinuous Galerkin methods


Publications (Google Scholar, arXiv)

• An Eulerian finite element method for the linearized Navier-Stokes problem in an evolving domain
  M. Neilan and M. Olshanskii
  Submitted
  [preprint]
• A tangential and penalty-free finite element method for the surface Stokes problem
  A. Demlow and M. Neilan
  Submitted
  [preprint]
• Discrete elasticity exact sequences on Worsey-Farin splits
  S. Gong, J. Gopalakrishnan, J. Guzman, and M. Neilan
  Submitted
  [preprint]
• Convergence of Lagrange finite elements for Maxwell eigenvalue problem in 3D
  D. Boffi, S. Gong, J. Guzman, and M. Neilan
  IMA Journal of Numerical Analysis, to appear
  [preprint]
• A note on the shape regularity of Worsey-Farin splits
  S. Gong, J. Guzman, and M. Neilan
  Journal of Scientific Computing, 95(2), Paper No. 46, 2023
  [preprint | article]
• A stable and H1-conforming divergence-free finite element pair for the Stokes problem using isoparametric mappings
  M. Neilan, and M.B. Otus
  Calcolo, 60(3), Paper No. 37, 2023
  [article]
• A CutFEM divergence-free discretization for the Stokes problem
  H. Liu, M. Neilan, and M. Olshanskii
  ESAIM: Mathematical Modeling and Numerical Analysis, 57(1):143-165, 2023
  [preprint | article]
• A divergence-free finite element method for the Stokes problem with boundary correction
  H. Liu, M. Neilan, and M.B. Otus
  Journal of Numerical Mathematics, 31(2):105-123, 2023
  [preprint | article]
• Exact sequences on Worsey-Farin splits
  J. Guzman, A. Lischke and M. Neilan
  Mathematics of Computation, 91(338):2571-2608, 2022
  [preprint | article]
• The Scott-Vogelius method for the Stokes problem on anisotropic meshes
  K. Kean, M. Neilan, and M. Schneier
  International Journal of Numerical Analysis and Modeling, 19(2-3):157-174, 2022
  [preprint | article]
• Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits
  M. Fabien, J. Guzman, M. Neilan, and A. Zytoon
  Computer Methods in Applied Mechanics and Engineering, 390, 2022
  [preprint | article]
• Convergence of Lagrange finite elements for the Maxwell eigenvalue problem in 2D
  D. Boffi, J. Guzman, and M. Neilan
  IMA Journal of Numerical Analysis, 43(2):663-691, 2023
  [preprint | article]
• Divergence-free Scott-Vogelius elements on curved domains
  M. Neilan and M.B. Otus
  SIAM Journal on Numerical Analysis, 59(2):1090-1116, 2021
  [preprint | article]
• Connection between grad-div stabilized Stokes finite elements and divergence-free elements
  M. Neilan and A. Zytoon
  International Journal of Numerical Analysis and Modeling, 17(6):839-857, 2020
  [article]
• Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem
  A. Linke, C. Merdon, and M. Neilan
  Electronic Transactions on Numerical Analysis, 52:281-294, 2020
  [preprint | article]
• The Stokes Complex: A review of exactly divergence–free finite element pairs for incompressible flows
  M. Neilan
  75 Years of Mathematics of Computation, Contemporary Mathematics, volume 754, AMS
  [article]
• Exact sequences of Powell-Sabin splits
  J. Guzman, A. Lischke, and M. Neilan
  Calcolo, 57(13), 2020.
  [preprint | article]
• The Monge-Ampere equation
  M. Neilan, A.J. Salgado, and W. Zhang
  Handbook of Numerical Analysis, vol 21:105-219, 2020.
  [preprint | chapter]
• Exact smooth piecewise polynomial sequences on Alfeld splits
  G. Fu, J. Guzman, and M. Neilan
  Mathematics of Computation, 89(323):1059-1091, 2020
  [preprint | article]
• Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs
  M. Neilan and M. Wu
  Journal of Computational and Applied Mathematics, 356:358-376, 2019
  [preprint | article]
• Low-order Raviart-Thomas approximations of axisymmetric Darcy flow
  M. Neilan and A. Zytoon
  Journal of Mathematical Analysis and Applications, 473(2):905-917, 2019
  [preprint | article]
• Rates of convergence in W2p-norm for the Monge-Ampere equation
  M. Neilan and W. Zhang
  SIAM Journal on Numerical Analysis, 56(5):3099-3120, 2018
  [preprint | article]
• Inf-sup stable finite elements on barycentric refinements producing divergence-free approximations in arbitrary dimensions
  J. Guzman and M. Neilan
  SIAM Journal on Numerical Analysis, 56(5):2826-2844, 2018
  [preprint | article]
• Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem
  A. Linke, C. Merdon, M. Neilan, and F. Neumann
  Mathematics of Computation, 87(312):1543-1566, 2018
  [preprint | article]
• Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic PDEs
  X. Feng, M. Neilan, and S. Schnake
  Journal of Scientific Computing, 74(3):1651-1676, 2018
  [preprint | article]
• Macro Stokes elements on quadrilaterals
  M. Neilan and D. Sap
  International Journal of Numerical Analysis and Modeling, 15(4-5):729-745, 2018
  [preprint | article]
• Convergence analysis of a finite element method for second order non-variational elliptic problems
  M. Neilan
  Journal of Numerical Mathematics, 25(3):169-184, 2017
  [preprint | article]
• A connection between coupled penalty projection timestepping schemes with FE spatial discretization for the Naiver-Stokes equations
  A. Linke, M. Neilan, L.G. Rebholz, and N.E. Wilson
  Journal of Numerical Mathematics, 25(4):229-248, 2017
  [preprint | article]
• On the divergence constraint in mixed finite element methods for incompressible flows
  V. John, A. Linke, C. Merdon, M. Neilan, and L.G. Rebholz
  SIAM Review, 59(3):492-544, 2017
  [preprint | article]
• A posteriori estimates using auxiliary subspace techniques
  H. Hakula, M. Neilan, and J.S. Ovall
  Journal of Scientific Computing, 72(1):97-127, 2017
  [preprint | article]
• Numerical analysis of strongly nonlinear PDEs
  M. Neilan, A.J. Salgado and W. Zhang
  Acta Numerica, 26:137-303, 2017
  [preprint | article]
• A C0 interior penalty method for a von Karman plate
  S.C. Brenner, M. Neilan, A. Reiser, and L.-Y. Sung
  Numerische Mathematik, 135(3):803-832, 2017
  [preprint | article]
• Finite element methods for second order linear elliptic partial differential equations in non-divergence form
  X. Feng, L. Hennings, and M. Neilan
  Mathematics of Computation, 86(307):2025-2051, 2017
  [preprint | article]
• Dual-mixed finite element methods for the stationary Boussinesq problem
  E. Colmenares and M. Neilan
  Computers and Mathematics with Applications, 72(7):1828-1850, 2016
  [preprint | article]
• Stable discontinuous Galerkin FEM without penalty parameters
  L. John, M. Neilan, and I. Smears
  Numerical Mathematics and Advanced Applications ENUMATH 2015.
  Lecture Notes in Computational Science and Engineering, vol 112:165-174
  [preprint | article]
• A dual mixed finite element method for the Brinkman problem
  J.S. Howell, M. Neilan, and N.J. Walkington
  SMAI Journal of Computational Mathematics, 2:1-17, 2016
  [preprint | article]
• DG finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations
  X. Feng, M. Neilan, and T. Lewis
  Journal of Computational and Applied Mathematics, 299:68-91, 2016
  [preprint | article]
• Stokes elements on cubic meshes yielding divergence-free approximations
  M. Neilan and D. Sap
  Calcolo, 53(3):263-283, 2016
  [preprint | article]
• Discrete and conforming smooth de Rham complexes in three dimensions
  M. Neilan
  Mathematics of Computation, 84(295):2059-2081, 2015
  [preprint | article]
• Finite element methods for fully nonlinear second order PDEs based on the discrete Hessian
  M. Neilan
  Journal of Computational and Applied Mathematics, 263:351-369, 2014
  [preprint | article]
• Finite element approximations of general fully nonlinear second order elliptic partial differential equations based on the vanishing moment method
  M. Neilan and X. Feng
  Computers and Mathematics with Applications, 68(12):2182-2204, 2014
  [preprint | article]
• A C0 method for the biharmonic problem without extrinsic penalization
  S.B.G. Karakoc and M. Neilan
  Numerical Methods for Partial Differential Equations, 30(4):1254-1278, 2014
  [preprint | article]
• Convergence analysis of a symmetric dual-wind discontinuous Galerkin method
  M. Neilan and T. Lewis
  Journal of Scientific Computing, 59(3):602-625, 2014
  [preprint | article]
• Conforming and divergence-free Stokes elements in three dimensions
  J. Guzman and M. Neilan
  IMA Journal of Numerical Analysis, 34(4):1489-1508, 2014
  [preprint | article]
• Symmetric and conforming mixed finite elements for plane elasticity using rational bubbles
  J. Guzman and M. Neilan
  Numerische Mathematik, 126(1):153-171, 2014
  [preprint | article]
• Conforming and divergence-free Stokes elements on general triangular meshes
  J. Guzman and M. Neilan
  Mathematics of Computation, 83(285):15-36, 2014
  [preprint | article]
• Convergence analysis of a fourth order perturbation of the radially symmetric Monge-Ampere equation
  X. Feng and M. Neilan
  Applicable Analysis, 93(8):1626-1646, 2014
  [preprint | article]
• A unified analysis for three finite element methods for the Monge-Ampere equation
  M. Neilan
  Electronic Transactions on Numerical Analysis, 41:262-288, 2014
  [preprint | article]
• Quadratic finite element methods for the Monge-Ampere equation
  M. Neilan
  Journal of Scientific Computing, 54(1):200-226, 2013
  [preprint | article]
• Stokes complexes and the construction of stable finite element methods with pointwise mass conservation
  R. Falk and M. Neilan
  SIAM Journal on Numerical Analysis, 51(2):1308-1326, 2013
  [preprint | article]
• Recent developments in numerical methods for fully nonlinear second order partial differential equations
  X. Feng, R. Glowinski, and M. Neilan
  SIAM Review, 55(2):205-267, 2013.
  [preprint | article]
• Isoparametric C0 interior penalty methods for plate bending problems on smooth domains
  S.C. Brenner, M. Neilan, and L.-Y. Sung
  Calcolo, 50(1):35-67, 2013
  [preprint | article]
• Finite element approximations of the three dimensional Monge-Ampere equation
  S.C. Brenner and M. Neilan
  ESAIM: Mathematical Modeling and Numerical Analysis, 46(5):979-1001, 2012
  [preprint | article]
• A family of non-conforming elements for the Brinkman problem
  J. Guzman and M. Neilan
  IMA Journal of Numerical Analysis, 32(4):1484-1508, 2012
  [preprint | article]
• A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem
  J. Guzman, D. Leykekhman, and M. Neilan
  Calcolo, 49(2):95-125, 2012
  [preprint | article]
• Error analysis of Galerkin approximations of the fully nonlinear Monge-Ampere equation
  X. Feng and M. Neilan
  Journal of Scientific Computing, 47:303-327, 2011
  [preprint | article]
• C0 penalty methods for the fully nonlinear Monge-Ampere equation
  S.C. Brenner, T. Gudi, M. Neilan, and L.-Y. Sung
  Mathematics of Computation, 80:1979-1995, 2011
  [preprint | article]
• C0 penalty methods for a fourth order elliptic singular perturbation problem
  S.C. Brenner and M. Neilan
  SIAM Journal on Numerical Analysis, 49:869-892, 2011
  [preprint | article]
• An interior penalty method for a sixth order elliptic equation
  T. Gudi and M. Neilan
  IMA Journal of Numerical Analysis, 31:1734-1753, 2011
  [preprint | article]
• Localized pointwise error estimates and global Lp error estimates of Nitsche’s method
  M. Neilan
  International Journal of Numerical Analysis, Series B, 2(4):338-354, 2011
  [preprint | article]
• Discontinuous Galerkin methods for a bi-wave equation modeling d-wave superconductors
  X. Feng and M. Neilan
  Mathematics of Computation 30:1303-1333, 2011
  [preprint | article]
• A nonconforming Morley finite element method for the Monge-Ampere equation
  M. Neilan
  Numerische Mathematik, 115(3):371-394, 2010
  [preprint | article]
• Finite element methods for a bi-wave equation modeling d-wave superconductors
  X. Feng and M. Neilan
  Journal of Computational Mathematics, 28(3):331-353, 2010
  [preprint | article]
• A modified characteristic finite element method for a fully nonlinear formulation of the semigeostrophic flow equations
  X. Feng and M. Neilan
  SIAM Journal on Numerical Analysis, 47(4):2952-2981, 2009
  [preprint | article]
• Mixed finite element approximations of the fully nonlinear Monge-Ampere equation based on the vanishing moment method
  X. Feng and M. Neilan
  SIAM Journal on Numerical Analysis, 47(2):1226-1250, 2009
  [preprint | article]
• Vanishing moment method and moment solutions for second order fully nonlinear partial differential equations
  X. Feng and M. Neilan
  Journal of Scientific Computing, 38(1):74-98, 2009
  [preprint | article]
• Error analysis of finite element approximations of the inverse mean curvature flow arising from general relativity
  X. Feng, M. Neilan, and A. Prohl
  Numerische Mathematik, 108(1):93-119, 2007
  [preprint | article]