Donald A. French
Current research is on mathematics problems
involving partial differential equations with applications in
neuronal networks, biofilms
and the spread of alcohol abuse.
See the Mathematical Modeling and
Scientific Computation in the Biosciences web page.
See also Applied Mathematics
Seminar web page.
Past and some continuing research is on error analysis for
finite element methods for partial differential equations
including finite element and meshfree schemes.
Also a part-time contractor at the Wright-Patterson Air Force
Base in Dayton, OH.
Permanent position is at the
University of Cincinnati.
Visiting Assistant Professor at Purdue University (1985-7),
Assistant Professor at Carnegie Mellon (1987-90), Visiting Professor
at University of Maryland Baltimore County (1995-6), and a visitor
at University of Minnesota (1997-8).
Graduate student in applied mathematics
obtained Ph.D. in 1985.
Thesis advisor was Lars B. Wahlbin.
See Curriculum Vita for more information.
- Jiyeon Oh (2000-2005)
(Assistant Professor at Tennessee State (2009-Present).
(Rollins College, Orlando, FLa.)
- Mauricio L. Osorio (2007-2010).
de Colombia, Medellín, Colombia in 2010.)
- Jhules Clack (2005-2014)
Suayip Toprakseven (2009-2014)
(Artvin Coruh University, Turkey).
Selected Recent Publications:
Clustering of CNG channels in the cilia of frog olfactory receptor
neurons (with R. Flannery and S.J. Kleene), Biophys.
J., 91 (2006), 179-188.
An Integrate-and-Fire Model for Synchronized Bursting in a Network of
Cultured Cortical Neurons (with E. Gruenstein), J. Comp.
Neurosci., 21 (2006), 227-241.
Identification of a free energy functional in an integro-differential equation
model for neuronal activity, Appl. Math. Lett., 17 (2004), 1047-1051.
Continuum models of the spread of alcoholism (with R. Braun, Z. Teymuorglu
and T. Lewis), Journal of Integral Equations and Applications,
22 (2010), 441-462.
Analysis of the convergence behavior of the localized nonlinear
approximation for electromagnetic scattering, J. Comp. Appl. Math.,
161 (2003), 27-39.
Error Analysis of Numerical Methods for PDE's
Finite element approximation of solutions to a class of nonlinear
hyperbolic-parabolic equations, (with S. Jensen and T. Seidman),
Appl. Numer. Math., 31 (1999), 429-450.
Error Analysis of a Modified Discontinuous Galerkin Recovery Scheme for
Diffusion Problems (with M. C. Galbraith and M. Osorio),
Applied Mathematics and Computation, (2012),
Error estimates for an element free Galerkin method with diffuse
derivatives and penalty stabilization (with Mauricio Osorio),
Computational Mechanics, doi 10.1007/s00466-012-0697-7.