Gerard Awanou Selected Publications in Reverse Chronological Order
Last modified January 22, 2021
Papers published or accepted
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.
Mixed finite elements for elasticity on quadrilateral meshes
with D. Arnold and F. Qiu. Advances in Comp. Math. 41, 553-572, 2015.
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.
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.
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.
Finite Element Differential Forms on Cubical Meshes, with D. Arnold, Mathematics of Computation 83, 1551-1570, 2014.
Rectangular Mixed Elements for Elasticity with Weakly Imposed Symmetry
. Adv. Comput. Math., 38, 2, 351-367, 2013.
Two remarks on rectangular mixed finite elements for elasticity
, J. of Scientific Computing, 50, 1, 91-102 2012.
The Serendipity Family of Finite Elements
, with D. Arnold.
Found. Comput. Math., 11, 337-344, 2011.
Symmetric Matrix Fields in the Finite Element Method
Symmetry, 2(3), pp. 1375-1389, 2010.
A Rotated Nonconforming Rectangular Mixed Finite Element for Elasticity.
Calcolo 46.1, pp. 49--60, 2009.
Robustness of a Spline Element Method
Journal of Scientific Computing, Vol. 36, Issue 3, pp. 421--432, 2008.
Finite elements for symmetric tensors in three dimensions
with D. Arnold and R. Winther.
Math. Comp. 77, 1229-1251, 2008.
Shortfall Risk Minimization under Regime Switching: Discrete Model
, Decisions in Economics and Finance, Volume 30, Number 1,
pp 71--78, May 2007.
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.
Rectangular Mixed Finite Elements for Elasticity
, with D. Arnold.
Math. Models and Methods in Appl. Sci. 15, 1417-1429, 2005.
Trivariate Spline Approximations of
the 3D Navier-Stokes Equations
with M.J. Lai. Mathematics of Computation 74, 585-601, 2005.
On Convergence Rate of the Augmented
Algorithm for Nonsymmetric
Saddle Point Problems
, with M.J. Lai.
Appl. Numer. Math. 54, no. 2, 122-134, 2005.
C^1 Quintic Spline Interpolation over
Tetrahedral Partitions ,
with M.J. Lai, in
Approximation Theory 10: Wavelets, Splines and
edited by C.K. Chui, L.L. Schumaker and J. Stoeckler,
Vanderbilt Univ. Press, pp. 1-16, 2002.
Reports available online and submitted papers
Energy Methods in 3D Spline Approximations of
. Ph. D. Dissertation, University of Georgia, Athens, Ga, Spring 2003.