University of Colorado Denver College of Liberal Arts and Sciences

Bio

Dr. Franca’s publication record includes works on stabilized methods, Galerkin least squares methods, unusual stabilized methods, residual-free bubbles, discontinuous enrichment methods and Petrov-Galerkin enrichment methods. He published over 100 papers in journals and conference proceedings. His body of work has received over 3,900 citations according to the ISI Web of Knowledge and he is now listed as an ISI Highly Cited Author. Dr. Franca is the recipient of the Young Investigator award sponsored by the US Association for Computational Mechanics. He was also elected Fellow by the US and the International Associations for Computational Mechanics. since 1999.

Select Publications

2005 - L.P. Franca, J.V.A. Ramalho and F. Valentin, "Multiscale and residual-free bubble functions for reaction-advection-diffusion problems." International Journal for Multiscale Computational Engineering 3: 297-312.

2006 - L.P. Franca, G. Hauke and A. Masud, "Revisiting stabilized finite element methods for the advective-diffusive equation." Computer Methods in Applied Mechanics and Engineering
195: 1560-1572.

2006 - L.P. Franca, J.V.A. Ramalho and F. Valentin, "Enriched Finite Element Methods for Unsteady Reaction-Diffusion Problems." Communications in Numerical Methods in Engineering,
22: 619-626.

2007 - L.P. Franca, S.P. Oliveira and M. Sarkis, "Continuous $Q_1-Q_1$ Stokes elements stabilized with non-conforming null edge average velocity functions." Mathematical Models and
Methods in Applied Sciences, 17: 439-459.

2007 - G.R. Barrenechea, L.P. Franca and F. Valentin, "A Petrov-Galerkin enriched method: A mass conservative finite element method for the Darcy equation," Computer Methods in Applied Mechanics and Engineering, 196: 2449-2464.

2007 - L.P. Franca, V. John, G. Matthies and L. Tobiska, "An inf-sup stable and residual-free bubble element for the Oseen equations," SIAM Journal on Numerical Analysis, 45: 2392-2407.

2008 - A. Masud and L.P. Franca, "A hierarchical multiscale framework for problems with \break
multiscale source terms," Computer Methods in Applied Mechanics and Engineering,
197: 2692-2700.

2008 - J.E. Dolbow and L.P. Franca, "Residual-free bubbles for embedded Dirichlet problems,"
Computer Methods in Applied Mechanics and Engineering, 197: 3751-3759.

2009 - R. Araya, G.R. Barrenechea, L.P. Franca and F. Valentin, "Stabilization arising from PGEM: A review and further developments," Applied Numerical Mathematics, 59: 2065-2081.

2009 - L.P. Franca, C. Harder and F. Valentin, "On a residual local projection method for the Darcy equation," C.R. Acad. Sci. Paris, 347: 1105-1110.

2009 - G.R. Barrenechea, L.P. Franca and F. Valentin, "A symmetric nodal conservative finite element method for the Darcy equation." SIAM J. Num. Analysis, 47: 3652-3677.

Courses Taught

MATH 3200: Introduction to Differential Equations
MATH 5660: Numerical Analysis I
MATH 5661: Numerical Analysis II
MATH 5663: Intro to FEM