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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(with X. Feng). SIAM Journal on Numerical Analysis, 47(2):1226-1250, 2009. - A modified characteristic finite element method for a fully nonlinear formulation of the semigeostrophic flow equations

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Numerische Mathematik, 115(3):371-394, 2010. - Finite element methods for a bi-wave equation modeling d-wave superconductors

(with X. Feng). Journal of Computational Mathematics, 28(3):331-353, 2010. - 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. - An interior penalty method for a sixth order elliptic equation

(with T. Gudi). IMA Journal of Numerical Analysis, 31:1734-1753, 2011. - 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. - Error analysis of Galerkin approximations of the fully nonlinear Monge-Ampere equation

(with X. Feng). Journal of Scientific Computing, 47:303-327, 2011. - C0 penalty methods for a fourth order elliptic singular perturbation problem

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(with X. Feng). arxiv.org/abs/1109.1183, 2011. - Localized pointwise error estimates and global Lp error estimates of Nitsche’s method

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Journal of Scientific Computing, 54(1):200-226, 2013. - 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. - 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. - Conforming and divergence-free Stokes elements on general triangular meshes

(with J. Guzman). Mathematics of Computation, 83(285):15-36, 2014 - Symmetric and conforming mixed finite elements for plane elasticity using rational bubbles

(with J. Guzman). Numerische Mathematik, 126(1):153-171, 2014. - Convergence analysis of a symmetric dual-wind discontinuous Galerkin method

(with T. Lewis). Journal of Scientific Computing, 59(3):602-625, 2014. - Convergence analysis of a fourth order perturbation of the radially symmetric Monge-Ampere equation

(with X. Feng). Applicable Analysis, 93(8):1626-1646, 2014. - Conforming and divergence-free Stokes elements in three dimensions

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(with X. Feng). Computers and Mathematics with Applications (to appear). - DG finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations

(with X. Feng and T. Lewis). Submitted. - 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. - A posteriori estimates using auxiliary subspace techniques

(with H. Hakula and J.S. Ovall). Submitted. - Stokes elements on cubic meshes yielding divergence-free approximations

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