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.

- (45) Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem

(with A. Linke, C. Merdon, and F. Neumann). Submitted. - (44) Macro Stokes elements on quadrilaterals

(with D. Sap). Submitted. - (43) Numerical analysis of strongly nonlinear PDEs

(with A.J. Salgado and W. Zhang). Submitted. - (42) Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic PDEs

(with X. Feng and S. Schnake). Submitted. - (41) A posteriori estimates using auxiliary subspace techniques

(with H. Hakula and J.S. Ovall). Journal of Scientific Computing (to appear). - (40) Dual-mixed finite element methods for the stationary Boussinesq problem

(with E. Colmenares). Computers and Mathematics with Applications, 72(7):1828-1850, 2016. - (39) On the divergence constraint in mixed finite element methods for incompressible flows

(with V. John, A. Linke, C. Merdon, and L.G. Rebholz). SIAM Review (to appear). - (38) 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). Journal of Numerical Mathematics (to appear). - (37) A C0 interior penalty method for a von Karman plate

(with S.C. Brenner, A. Reiser, and L.-Y. Sung). Numerische Mathematik, Numerische Mathematik, 135(3):803-832, 2017. - (36) A dual mixed finite element method for the Brinkman problem

(with J.S. Howell and N.J. Walkington). SMAI Journal of Computational Mathematics, 2:1-17, 2016. - (35) Finite element methods for second order linear elliptic partial differential equations in non-divergence form

(with X. Feng and L. Hennings). Mathematics of Computation (to appear). - (34) Convergence analysis of a finite element method for
second order non-variational elliptic problems

Journal of Numerical Mathematics (to appear). - (33) Stable discontinuous Galerkin FEM without penalty parameters

(with L. John and I. Smears). Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112:165-174. - (32) DG finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations

(with X. Feng and T. Lewis). Journal of Computational and Applied Mathematics, 299:68-91, 2016. - (31) Stokes elements on cubic meshes yielding divergence-free approximations

(with D. Sap). Calcolo, 53(3):263-283, 2016. - (30) Discrete and conforming smooth de Rham complexes in three dimensions

Mathematics of Computation, 84(295):2059-2081, 2015. - (29) Finite element methods for fully nonlinear second order PDEs based on the discrete Hessian

Journal of Computational and Applied Mathematics, 263:351-369, 2014. - (28) 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. - (27) 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. - (26) Convergence analysis of a symmetric dual-wind discontinuous Galerkin method

(with T. Lewis). Journal of Scientific Computing, 59(3):602-625, 2014. - (25) Conforming and divergence-free Stokes elements in three dimensions

(with J. Guzman). IMA Journal of Numerical Analysis, 34(4):1489-1508, 2014 - (24) Symmetric and conforming mixed finite elements for plane elasticity using rational bubbles

(with J. Guzman). Numerische Mathematik, 126(1):153-171, 2014. - (23) Conforming and divergence-free Stokes elements on general triangular meshes

(with J. Guzman). Mathematics of Computation, 83(285):15-36, 2014 - (22) Convergence analysis of a fourth order perturbation of the radially symmetric Monge-Ampere equation

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(with X. Feng). arxiv.org/abs/1109.1183, 2011. - (12) Error analysis of Galerkin approximations of the fully nonlinear Monge-Ampere equation

(with X. Feng). Journal of Scientific Computing, 47:303-327, 2011. - (11) 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. - (10) C0 penalty methods for a fourth order elliptic singular perturbation problem

(with S.C. Brenner). SIAM Journal on Numerical Analysis, 49:869-892, 2011. - (9) An interior penalty method for a sixth order elliptic equation

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- Susanne C. Brenner
- Richard S. Falk
- Xiaobing H. Feng
- Roland Glowinski
- Thirupathi Gudi
- Johnny Guzman
- Harri Hakula
- Jason S. Howell
- Lorenz John
- Volker John
- Thomas Lewis
- Dmitriy Leykekhman
- Alexander Linke
- Christian Merdon
- Jeffrey S. Ovall
- Leo Rebholz
- Abner Salgado
- Iain Smears
- Li-yeng Sung
- Noel Walkington
- Wujun Zhang