This material is based upon work supported by the National Science Foundation through grants DMS-1238711/1115421, DMS-0902683, DMS-1417980. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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differential equations in non-divergence form

(with X. Feng and L. Hennings), sumbitted - (35) Finite element methods for fully nonlinear second order PDEs based on the discrete Hessian

Journal of Computational and Applied Mathematics, 263:351-369, 2014. - (34) Finite element approximations of general fully nonlinear second order elliptic partial differential equations based on the vanishing moment method

(with X. Feng). Computers and Mathematics with Applications, 68(12):2182-2204, 2014. - (33) Convergence analysis of a fourth order perturbation of the radially symmetric Monge-Ampere equation

(with X. Feng). Applicable Analysis, 93(8):1626-1646, 2014. - (32) A unified analysis for three finite element methods for the Monge-Ampere equation

Electronic Transactions on Numerical Analysis, 41:262-288, 2014. - (31) Quadratic finite element methods for the Monge-Ampere equation

Journal of Scientific Computing, 54(1):200-226, 2013. - (30) Recent developments in numerical methods for fully nonlinear second order partial differential equations

(with X. Feng and R. Glowinski). SIAM Review, 55(2):205-267, 2013. - (29) Finite element approximations of the three dimensional Monge-Ampere equation

(with S.C. Brenner). ESAIM: Mathematical Modeling and Numerical Analysis, 46(5):979-1001, 2012. - (28) The vanishing moment method for fully nonlinear second order partial differential equations: formulation, theory, and numerical analysis

(with X. Feng). arxiv.org/abs/1109.1183, 2011. - (27) Error analysis of Galerkin approximations of the fully nonlinear Monge-Ampere equation

(with X. Feng). Journal of Scientific Computing, 47:303-327, 2011. - (26) C0 penalty methods for the fully nonlinear Monge-Ampere equation

(with S.C. Brenner, T. Gudi and L.-Y. Sung). Mathematics of Computation, 80:1979-1995, 2011. - (25) A nonconforming Morley finite element method for the Monge-Ampere equation

Numerische Mathematik, 115(3):371-394, 2010. - (24) A modified characteristic finite element method for a fully nonlinear formulation of the semigeostrophic flow equations

(with X. Feng). SIAM Journal on Numerical Analysis, 47(4):2952-2981, 2009. - (23) Error analysis for mixed finite element approximations of the fully nonlinear Monge-Ampere equation based on the vanishing moment method

(with X. Feng). SIAM Journal on Numerical Analysis, 47(2):1226-1250, 2009. - (22) Vanishing moment method and moment solutions for second order fully nonlinear partial differential equations

(with X. Feng). Journal of Scientific Computing, 38(1):74-98, 2009. - (21) Stokes elements on cubic meshes yielding divergence-free approximations

(with D. Sap). Submitted. - (20) Discrete and conforming smooth de Rham complexes in three dimensions

Mathematics of Computation (to appear). - (19) Conforming and divergence-free Stokes elements in three dimensions

(with J. Guzman). IMA Journal of Numerical Analysis, 34(4):1489-1508, 2014 - (18) Symmetric and conforming mixed finite elements for plane elasticity using rational bubbles

(with J. Guzman). Numerische Mathematik, 126(1):153-171, 2014. - (17) Conforming and divergence-free Stokes elements on general triangular meshes

(with J. Guzman). Mathematics of Computation, 83(285):15-36, 2014 - (16) Stokes complexes and the construction of stable finite element methods with pointwise mass conservation

(with R. Falk). SIAM Journal on Numerical Analysis, 51(2):1308-1326, 2013. - (15) A family of non-conforming elements for the Brinkman problem

(with J. Guzman). IMA Journal of Numerical Analysis, 32(4):1484-1508, 2012. - (14) DG finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations

(with X. Feng and T. Lewis). Submitted. - (13) A C0 method for the biharmonic problem without penalty

(with S.B.G. Karakoc). Numerical Methods for Partial Differential Equations, 30(4):1254-1278, 2014. - (12) Convergence analysis of a symmetric dual-wind discontinuous Galerkin method

(with T. Lewis). Journal of Scientific Computing, 59(3):602-625, 2014. - (11) Isoparametric C0 interior penalty methods for plate bending problems on smooth domains

(with S.C. Brenner and L.-Y. Sung). Calcolo, 50(1):35-67, 2013. - (10) A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem

(with J. Guzman and D. Leykekhman). Calcolo, 49(2):95-125, 2012. - (9) C0 penalty methods for a fourth order elliptic singular perturbation problem

(with S.C. Brenner). SIAM Journal on Numerical Analysis, 49:869-892, 2011. - (8) An interior penalty method for a sixth order elliptic equation

(with T. Gudi). IMA Journal of Numerical Analysis, 31:1734-1753, 2011. - (7) Localized pointwise error estimates and global Lp error estimates of Nitsche’s method

International Journal of Numerical Analysis, Series B, 2(4):338-354, 2011. - (6) Nonconforming finite element and discontinuous Galerkin methods for a bi-wave equation modeling d-wave superconductors

(with X. Feng). Mathematics of Computation 30:1303-1333, 2011. - (5) A posteriori estimates using auxiliary subspace techniques

(with H. Hakula and J.S. Ovall). Submitted. - (4) A C0 interior penalty method for a von Karman plate

(with S.C. Brenner, A. Reiser, and L.-Y. Sung). Submitted. - (3) Improving efficiency of coupled schemes for Navier-Stokes equations by a connection to grad-div stabilized projection methods

(with A. Linke, L.G. Rebholz, and N.E. Wilson). Submitted. - (2) Finite element methods for a bi-wave equation modeling d-wave superconductors

(with X. Feng). Journal of Computational Mathematics, 28(3):331-353, 2010. - (1) Error analysis of finite element approximations of the inverse mean curvature flow arising from general relativity

(with X. Feng and A. Prohl). Numerische Mathematik, 108(1):93-119, 2007.