- Rates of convergence in W2p-norm for the Monge-Ampere equation

N. Neilan and W. Zhang

*Submitted*

[preprint]

Inf-sup stable finite elements on barycentric refinements producing divergence-free approximations in arbitrary dimensions

J. Guzman and M. Neilan

*Submitted*

[preprint]- Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs

M. Neilan and M. Wu

*Submitted*

[preprint] - 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 (to appear)*

[preprint] - 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 (to appear)*

[preprint] - Macro Stokes elements on quadrilaterals

M. Neilan and D. Sap

*International Journal of Numerical Analysis and Modeling (to appear)*

[preprint] - 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] - Improving efficiency of coupled schemes for Navier-Stokes equations by a connection to grad-div stabilized projection methods

A. Linke, M. Neilan, L.G. Rebholz, and N.E. Wilson

*Journal of Numerical Mathematics (to appear)*

[preprint] - 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]