Gerard Awanou Publications

Last Modified, September 18, 2011

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

Finite Element Methods

The Serendipity Family of Finite Elements , with D. Arnold. Found. Comput. Math., 11:337-344, 2011.

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 , To appear in J. of Scientific Computing, 2011.
Rectangular Mixed Elements for Elasticity with Weakly Imposed Symmetry Condition, , Accepted for publication in Advances in Computational Mathematics, 2011.

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.
Trivariate Spline Approximation of Divergence-Free Vector Fields, with M.J. Lai. Preprint 2004.
Spline Element Method for Monge-Ampere Equations. Preprint 2010.
Pseudo time continuation and time marching methods for Monge-Ampere type Equations . In revision.

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.
Multiscale Asymptotics of Partial Hedging . Preprint, 2004.
Super-Replication of Contingent Claims on Stocks with Regime Switching Fluctuations . Preprint, 2004.