Gerard Awanou Selected Publications

Last Modified, January 22, 2021

Energy Methods in 3D Spline Approximations of Navier-Stokes equations . Ph. D. Dissertation, University of Georgia, Athens, Ga, Spring 2003.

Fully nonlinear equations

  • Computational nonimaging geometric optics: Monge-Ampere Notices of the American Mathematical Society February 2021 Volume 68, No 2, pp. 186--193.
  • A two-grid method for the C0 interior penalty discretization of the Monge-Ampere equation (with Hengguang Li and Eric Malitz) J. of Comp. Math. 38, No 4, (2020) pp. 547-564.
  • Iterative methods for k-Hessian equations Methods and Applications of Analysis, Vol. 25, No. 1 (2018), pp. 51-72.
  • Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: Aleksandrov solutions ESAIM: M2AN, 51, 707-725, 2017.
  • Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation. Symmetry 2016, 8, 18.
  • On Standard finite difference discretizations of the elliptic Monge-Ampere equation. Journal of Scientific Computing, 69, 2, 892-904, 2016.
  • Convergence of finite difference schemes to the Aleksandrov solution of the Monge-Ampere equation (with Romeo Awi) Acta Applicandae Mathematicae 144-1, 87-98, 2016.
  • Quadratic mixed finite element approximations of the Monge-Ampere equation in 2D. Calcolo 52, 503-518, 2015. Erratum in Calcolo, 54, 1, 281-297, 2017.
  • Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: Classical solutions. IMA J. Numer. Anal. 35 (2015), no. 3, 1150-1166.
  • Pseudo transient continuation and time marching methods for Monge-Ampere type Equations, Advances in Comp. Math. 41, 907-935, 2015.
  • Spline Element Method for Monge-Ampere Equations , B.I.T. Num. Analysis. 55, 625-646, 2015.
  • Smooth approximations of the Aleksandrov solution of the Monge-Ampere equation , Communications in Math. Sc. 13, 427-441, 2015.
  • Isogeometric method for the elliptic Monge-Ampere equation, in Approximation Theory, XIV (San Antonio, TX, 2013), edited by G.E. Fasshauer and L.L. Schumaker, Springer, 1-13, 2014.
  • Error analysis of a mixed finite element method for the Monge-Ampere equation, with H. Li, Int. J. Numerical Analysis and Modeling, 11, 4, 745-761, 2014.

    Canonical Finite Element Methods

    The Serendipity Family of Finite Elements , with D. Arnold. Found. Comput. Math., 11, 337-344, 2011.
    Finite Element Differential Forms on Cubical Meshes, with D. Arnold, Mathematics of Computation 83, 1551-1570, 2014.

    Mixed Finite Elements for Elasticity

    Rectangular Mixed Finite Elements for Elasticity , with D. Arnold. Math. Models and Methods in Appl. Sci. 15, 1417-1429, 2005.
    Finite elements for symmetric tensors in three dimensions with D. Arnold and R. Winther. Math. Comp. 77, 1229-1251, 2008.
    A Rotated Nonconforming Rectangular Mixed Finite Element for Elasticity, , Calcolo 46.1, pp. 49--60, 2009.
    Symmetric Matrix Fields in the Finite Element Method , Symmetry, 2(3), pp. 1375-1389, 2010.
    Two remarks on rectangular mixed finite elements for elasticity , J. of Scientific Computing, 50, 1, 91-102 2012.
    Rectangular Mixed Elements for Elasticity with Weakly Imposed Symmetry Condition, Adv. Comput. Math. 38, no. 2, 351-367, 2013.
    Nonconforming tetrahedral mixed finite elements for elasticity, with D. Arnold and R. Winther, Math. Models and Methods in Appl. Sciences, 24, 4, 783-796, 2014.
    Mixed finite elements for elasticity on quadrilateral meshes with D. Arnold and F. Qiu. Advances in Comp. Math. 41, 553-572, 2015.

    Multivariate Spline Method for Numerical Solution of Partial Differential Equations

    Trivariate Spline Approximations of the 3D Navier-Stokes Equations , with M.J. Lai. Mathematics of Computation 74, 585-601, 2005.
    The Multivariate Spline Method for Scattered Data Fitting and Numerical Solution of Partial Differential Equations, with M.J. Lai and P. Wenston in Wavelets and Splines: Athens 2005, edited by G. Chen and M. J. Lai, Nashboro Press, 24-74, 2006.
    Robustness of a Spline Element Method with Constraints. Journal of Scientific Computing, Vol. 36, Issue 3, pp. 421--432, 2008.

    Iterative Methods

    On Convergence Rate of the Augmented Lagrangian Algorithm for Nonsymmetric Saddle Point Problems , with M.J. Lai. Appl. Numer. Math. 54, no. 2, 122-134, 2005.

    Scattered Data Interpolation Methods

    C^1 Quintic Spline Interpolation over Tetrahedral Partitions , with M.J. Lai, in Approximation Theory 10: Wavelets, Splines and Applications, edited by C.K. Chui, L.L. Schumaker and J. Stoeckler, Vanderbilt Univ. Press, pp. 1-16, 2002.

    Mathematical Finance

    Shortfall Risk Minimization under Regime Switching: Discrete Model , Decisions in Economics and Finance, Volume 30, Number 1, pp 71--78, May 2007.


    Reports available online and submitted papers