Gerard Awanou Selected Publications in Reverse Chronological Order
Last modified January 22, 2021
Papers published or accepted
Computational nonimaging geometric optics: MongeAmpere
Notices of the American Mathematical Society February 2021 Volume 68, No 2, pp. 186193.
A twogrid method for the C0
interior penalty discretization of the MongeAmpere equation
(with Hengguang Li and Eric Malitz) J. of Comp. Math. 38, No 4, (2020) pp. 547564.
Iterative methods for kHessian equations
Methods and Applications of Analysis, Vol. 25, No. 1 (2018), pp. 5172.
Standard finite elements for the numerical resolution of the elliptic MongeAmpere equation: Aleksandrov solutions
ESAIM: M2AN, 51, 707725, 2017.
Convergence Rate of a Stable, Monotone and Consistent Scheme for the MongeAmpĂ¨re Equation.
Symmetry 2016, 8, 18.
On Standard finite difference discretizations of the elliptic MongeAmpere equation.
Journal of Scientific Computing, 69, 2, 892904, 2016.
Convergence of finite difference schemes to the Aleksandrov solution of
the MongeAmpere equation (with Romeo Awi)
Acta Applicandae Mathematicae 1441, 8798, 2016.
Quadratic mixed finite element approximations of the MongeAmpere equation in 2D.
Calcolo 52, 503518, 2015. Erratum in Calcolo, 54, 1, 281297, 2017.
Standard finite elements for the numerical resolution of the elliptic MongeAmpere equation: Classical solutions.
IMA J. Numer. Anal. 35 (2015), no. 3, 11501166.
Pseudo transient continuation and time marching methods for MongeAmpere type Equations,
Advances in Comp. Math. 41, 907935, 2015.
Spline Element Method for MongeAmpere Equations
, B.I.T. Num. Analysis. 55, 625646, 2015.
Smooth approximations of the Aleksandrov solution of the MongeAmpere equation , Communications in Math. Sc. 13, 427441, 2015.
Mixed finite elements for elasticity on quadrilateral meshes
with D. Arnold and F. Qiu. Advances in Comp. Math. 41, 553572, 2015.
Error analysis of a mixed finite element method for the MongeAmpere equation,
with H. Li, Int. J. Numerical Analysis and Modeling, 11, 4, 745761, 2014.
Isogeometric method for the elliptic MongeAmpere equation,
in Approximation Theory, XIV (San Antonio, TX, 2013), edited by G.E. Fasshauer and L.L. Schumaker, Springer, 113, 2014.
Nonconforming tetrahedral mixed finite elements for elasticity, with D. Arnold and R. Winther, Math. Models and Methods in Appl. Sciences, 24, 4, 783796, 2014.
Finite Element Differential Forms on Cubical Meshes, with D. Arnold, Mathematics of Computation 83, 15511570, 2014.
Rectangular Mixed Elements for Elasticity with Weakly Imposed Symmetry
Condition
. Adv. Comput. Math., 38, 2, 351367, 2013.
Two remarks on rectangular mixed finite elements for elasticity
, J. of Scientific Computing, 50, 1, 91102 2012.
The Serendipity Family of Finite Elements
, with D. Arnold.
Found. Comput. Math., 11, 337344, 2011.
Symmetric Matrix Fields in the Finite Element Method
,
Symmetry, 2(3), pp. 13751389, 2010.
A Rotated Nonconforming Rectangular Mixed Finite Element for Elasticity.
,
Calcolo 46.1, pp. 4960, 2009.
Robustness of a Spline Element Method
with Constraints.
Journal of Scientific Computing, Vol. 36, Issue 3, pp. 421432, 2008.
Finite elements for symmetric tensors in three dimensions
with D. Arnold and R. Winther.
Math. Comp. 77, 12291251, 2008.
Shortfall Risk Minimization under Regime Switching: Discrete Model
, Decisions in Economics and Finance, Volume 30, Number 1,
pp 7178, May 2007.
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, 2474, 2006.
Rectangular Mixed Finite Elements for Elasticity
, with D. Arnold.
Math. Models and Methods in Appl. Sci. 15, 14171429, 2005.
Trivariate Spline Approximations of
the 3D NavierStokes Equations
,
with M.J. Lai. Mathematics of Computation 74, 585601, 2005.
On Convergence Rate of the Augmented
Lagrangian
Algorithm for Nonsymmetric
Saddle Point Problems
, with M.J. Lai.
Appl. Numer. Math. 54, no. 2, 122134, 2005.
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. 116, 2002.
Reports available online and submitted papers
Dissertation
Energy Methods in 3D Spline Approximations of
NavierStokes equations
. Ph. D. Dissertation, University of Georgia, Athens, Ga, Spring 2003.
