# Leopoldo Luis Cabo Penna Franca

### Quick Info

Born
7 April 1959
Rio de Janeiro, Brazil
Died
19 September 2012
Rio de Janeiro, Brazil

Summary
Leopoldo Franca was a Brazilian mathematician who had a major impact in the development and analysis of innovative finite element methods. He worked mainly on stabilised methods for fluids, acoustics and solids, residual-free methods, and enriched methods for transport equations.

### Biography

Leopoldo Penna Franca was the son of Leonel Penna and Marlene Franca. He was known to his family friends and colleagues as Leo. After attending primary and secondary schools in Rio de Janeiro, where he showed extraordinary abilities in mathematics and physics, he entered the Pontifical Catholic University in Rio de Janeiro to study mechanical engineering. The Pontifical Catholic University was founded in 1940 by the Roman Catholic Church becoming the first private higher education institution in Brazil. It gained university status in 1946 and began teaching graduate courses in 1963. It was particularly strong in mechanical engineering and in fact the first student to be awarded an M.Sc. in 1965 obtained a Mechanical Engineering degree. Let us note that he was the first student to be awarded a Master of Science Degree from a Brazilian Institution.

Franca began his studies at the Pontifical Catholic University in 1977 and was awarded his B.S. in mechanical engineering in 1981. He continued to undertake postgraduate studies advised by Francisco Eduardo Mourao. Mourao had been awarded a degree in Mechanical and Electrical Engineering from the Federal University of Minas Gerais in 1962, a Master's Degree in Aeronautical and Mechanical Engineering from the Instituto Tecnológico de Aeronáutica in 1968 and a PhD in Mechanical Engineering from the University of Minnesota in 1974. Franca had been awarded a CAPES fellowship to support his Master's Degree which he was awarded in 1983. CAPES is a Foundation within the Ministry of Education in Brazil whose central purpose is to coordinate efforts to improve the quality of Brazil's faculty and staff in higher education through grant programs. CAPES is particularly concerned with the training of doctoral candidates.

On 28 July 1983, Franca married Ana Cristina Leonardos (born 1 February 1960). Ana had studied at the Pontifical Catholic University of Rio de Janeiro from 1979 to 1983, being awarded a degree of Language-Literature (Portuguese and English) in 1983.

After the award of his Master's Degree, Franca wished to continue to study for a Ph.D. supported by CAPES and was able to undertake research at Stanford University in California, USA. At Stanford University, Franca's studies were supervised by Thomas Joseph Robert Hughes (born 1943). Hughes was awarded B.E. and M.E. degrees in Mechanical Engineering from Pratt Institute and an M.S. in Mathematics and a Ph.D. in Engineering Science from the University of California at Berkeley. Before being appointed to Stanford, he taught at the California Institute of Technology and the University of California, Berkeley. At Stanford he served as Chairman of the Division of Applied Mechanics, Chairman of the Department of Mechanical Engineering, Chairman of the Division of Mechanics and Computation, and held the Mary and Gordon Crary Chair of Engineering. Franca and his co-authors wrote the following in a celebration volume for the 60th birthday of Thomas J R Hughes [6]:-
Tom Hughes made pioneering contributions in many fronts in finite element methods and computational mechanics and has been a prime mover in bringing these fields to a new era. We see all of this in the contributions he made directly, in the contributions he made through the students he trained and associates he guided, and in the contributions made by the friends and colleagues he inspired.
Franca's wife Ana came to Stanford University with her husband and studied Master's courses in Education, then Master's courses in Sociology and undertook research for a Ph.D. in social sciences applied to education beginning in 1985.

Before the award of his Ph.D., Franca had over ten papers in print. His early papers were written with several fellow students and staff in the Division of Applied Mechanics, Durand Building, Stanford University. These included Franca's thesis advisor Thomas J R Hughes and Michel Mallet, Marc Balestra, Isaac Harari, together with the Brazilian post-doctoral student Abimael Fernando Dourado Loula who had been awarded his doctorate by the Federal University in Rio de Janeiro in 1979. Franca's first papers include: (i) T J R Hughes, L P Franca and M Balestra, A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal-Order Interpolations (1986); and (ii) T J R Hughes, L P Franca and M Mallet, A New Finite Element for Computational Fluid Dynamics: I. Symmetric Forms of the Compressible Euler and Navier-Stokes Equations and the Second Law of Thermodynamics (1986). These papers have, the following abstracts:-
(i) A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by $C_{0}$ interpolations. Combinations of $C_{0}$ interpolations which are unstable according to the Babuska-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behaviour of the methodology are presented.

(ii) Results of Harten and Tadmor are generalized to the compressible Navier-Stokes equations including heat conduction effects. A symmetric form of the equations is derived in terms of entropy variables. It is shown that finite element methods based upon this form automatically satisfy the second law of thermodynamics and that stability of the discrete solution is thereby guaranteed ab initio.
Franca was awarded a Ph.D. in 1987 for his thesis New Mixed Finite Element Methods. This has the following Abstract (see [8] or [9]):-
New finite element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least squares like terms. The additional terms involve integrals over element interiors, and include mesh dependent coefficients. The methods are designed to enhance stability. Consistence is achieved in the sense that exact solutions identically satisfy the variational equations. Applied to several problems, simple finite element interpolations are rendered convergent, including convenient equal order interpolations which are generally unstable within the Galerkin approach. The methods are divided into two classes according to the manner in which stability is attained: (1) Circumventing Babuska-Brezzi condition methods; (2) Satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods.
After the award of his doctorate, Franca spent a year as a postdoctoral researcher at the University of Stanford in the United States. In 1988, while Ana Leonardos continued to work on her Ph.D., the couple were divorced. From 1988 to 1993 Franca worked in the National Laboratory for Scientific Computing at the Department of Applied and Computational Mathematics of the Ministério da Ciência e Tecnologia. This was the first Brazilian institution in the field of scientific computing and computational modelling. He began attending conferences, for example the Fifth Brazilian Symposium on Piping and Pressure Vessels held at Salvador, Brazil in 1988. In the same year, he also attended the congress ENCIT organised by the Brazilian Association of Mechanical Sciences, and the Eleventh Congresso Nacional de Matemática Aplicada e Computacional held in Ouro Preto, Brazil. In the following year he attended the Pan American Congress of Applied Mechanics held in Rio De Janeiro in January 1989, the Fifth International Symposium on Numerical Methods in Engineering held at the Ecole Polytechnique Fédérale de Lausanne, Switzerland in September 1989, and the Seventh International Conference on Finite Element Methods in Flow Problems held at the University of Alabama, Huntsville in April 1989.

For title of lectures given by Franca at various conferences throughout his career and papers he published in journals, see THIS LINK.

On 16 May 1991, Franca married Lucia Valadao. They had two daughters, Louise and Lais.

In 1993 he went to Purdue University in West Lafayette, Indiana, USA as a Visiting Professor. Later in 1993 he was appointed as Visiting Professor at the University of Colorado at Denver. In 1994 he became an Associate Professor at the University of Colorado, then, two years later, he became the director of the Center for Computational Mathematics there. He was promoted to full professor in 1999. It was while he was at the University of Colorado, that he had a life-threatening health problem which came to a head in 2004 [1]:-
Leo struggled against a severe liver disease, caused by Wilson's disease, which required a liver transplant he could finally accomplish in 2004, at the University of Colorado Hospital. About this, he wrote on his Facebook page: 'It was a dramatic year. I spent one year waiting for a liver transplant. Towards the end I was having a series of liver failures until I completely passed out. The doctor told my wife I had three days to live, and he was hoping a liver would appear. It did! And all ended well!'
In 2008 he left the United States and returned to Brazil where he spent the years until 2010 as a Visiting Professor at the Civil Engineering Department of the Alberto Luiz Coimbra Institute for Graduate Studies and Research at the Federal University of Rio de Janeiro. There he became colleagues of José Luis Drummond Alves, Alvaro L G A Coutinho and Fernando Rochinha, the authors of [1], who write that during these two years:-
... he joined our team at the High Performance Computing Center at the Alberto Luiz Coimbra Institute for Graduate Studies and Research at the Federal University of Rio de Janeiro, collaborating as a consultant in Research and Development projects for the oil industry. Many fruitful meetings and discussions with Leo around themes such as fluid-structure interaction and its underlying intricacies provided deeper insight into the problem and, by all means, enjoyable moments to be remembered by all team members.
In 2011 he briefly joined National Laboratory for Scientific Computing at the Ministério da Ciência e Tecnologia but, later in the same year, he joined the new IBM Research Laboratory in Brazil, the first IBM Research Laboratory in the Southern Hemisphere. It was established in June 2010, with locations in São Paulo and Rio de Janeiro. Ulisses Mello, engineer and associate director at IBM Research, Brazil, led the Smarter Natural Resources & Discovery strategic group and it was this group that Franca joined as a senior research scientist. He worked on projects involving applications of computational mathematics and mechanics to the oil industry. While working for IBM, Franca was one of six members of staff who applied for a patent for Method to assess the impact of existing fractures and faults for reservoir management on 9 November 2012. Sadly Franca had died two months before the application for the patent was filed. The Abstract for the Patent reads [10]:-
Assessing the impact of existing fractures and faults for reservoir management, in one aspect, may comprise employing a numerical mesh to generate a geomechanical model, the numerical mesh representing a geological reservoir and its surrounding regions, the numerical mesh comprising delimitation associated with regions and layering of geology without constraining the numerical mesh to explicitly represent a fault or fracture, initialising the geomechanical model to define initial stress-strain compatible with measured stress in well locations associated with the geological reservoir, generating a fluid-flow model employing the numerical mesh, solving for a coupled solution of the fluid-flow model and the geomechanical model, and employing the solved fluid-flow model and the geomechanical model to assess the impact.
The Patent was granted on 12 July 2016.

The authors of [1] give this overview of the topics on which Franca worked:-
His experience in mechanical engineering with emphasis in numerical methods allowed him to act, among others, on the following subjects: stabilised methods for fluids, solids and acoustics, residual-free methods, and methods for enhanced transport equations. Leo's publication record includes works on stabilised methods, Galerkin least squares methods, unusual stabilised methods, residual-free bubbles, discontinuous enrichment methods, and Petrov-Galerkin enrichment methods.
You can see the range of his work from the titles of his papers at THIS LINK.

During his career, Franca received many awards. These included: the Outstanding Research Award from the University of Colorado Denver College of Liberal Arts and Sciences (1997 and 1999); and the R H Gallagher Young Investigator Award and Medal from the U.S. Association for Computational Mechanics (1999). He was elected a fellow of the International Association for Computational Mechanics in 2002 and a fellow of the U.S. Association for Computational Mechanics (2007). In 2005 he was listed as a Highly Cited Author in the Institute of Science Index. A search today (August 2022) of the Web of Science Index shows that Leopoldo P Franca is cited 7242 times. He was an active member of the Advisory Board of International Journal for Numerical Methods in Engineering and of Computer Methods in Applied Mechanics and Engineering.

Franca died suddenly following a heart attack in September 2012 at the age of 53. The authors of [7] write:-
Leo was a highly cited author ... and during his brilliant career he had a major impact in the development and analysis of innovative finite element methods. Leo ... was a generous, polite and funny friend who loved good food and travelling. He is survived by his wife Lucia and his two daughters Louise and Lais. He will be dearly missed by his several friends all over the world.

### References (show)

1. J L D Alves, A L G A Coutinho and F A Rochinha, Leopoldo Luis Cabo Penna Franca (April 7, 1959-September 19, 2012), International Journal for Numerical Methods in Engineering 93 (2) (2012), 135-136
2. Leopoldo Luis Cabo Penna Franca, escavador.com.
3. Leopoldo Penna Franca: mechanical engineer, prabook.com.
https://prabook.com/web/leopoldo_penna.franca/3397751
4. Leopoldo Penna Franca, American Men & Women of Science. A biographical directory of today's leaders in physical, biological and related sciences (Gale, Cengage Learning, Detroit, 2008).
5. Leopoldo Penna Franca, Who's Who in the World (Marquis Who's Who, New Providence, NJ, 1992).
6. L P Franca, T E Tezduyar and A Masud, Finite Element Methods: 1970's and Beyond (CIMNE, Barcelona, 2004).
7. A Madureira and F Valentin, Leo Franca, 1959-2012, NA Digest 12 (40) (Monday, 1 October 2012).
8. New Mixed Finite Element Methods, Scientific and Technical Aerospace Reports 26 (17) (1988), 2567.
9. New Mixed Finite Element Methods, Dissertation Abstracts International. The sciences and engineering (University Microfilms, 1988), 3335; 3453.
10. Patents by Inventor Leopoldo Luis Cabo Penna Franca, JUSTIA Patents.
https://patents.justia.com/inventor/leopoldo-luis-cabo-penna-franca