Profile (CV) of the research teaching staff

Gracia Lozano, José Luis
Department: Departamento de Matemática Aplicada
Field: Matemática Aplicada
Faculty: Escuela de Ingeniería y Arquitectura

Research Institute: INSTITUTO UNIVERSITARIO DE MATEMÁTICAS Y APLICACIONES (IUMA)
Group: E24_23R: APEDIF (Aplicaciones de Ecuaciones Diferenciales)

UNESCO codes
  • Ecuaciones íntegro-diferenciales
  • Ecuaciones diferenciales ordinarias
  • Ecuaciones diferenciales en derivadas parciales

Number of 6-year periods of research productivity evaluation
  • CNEAI research evaluation. 01/01/24
  • CNEAI research evaluation. 01/01/18
  • CNEAI research evaluation. 01/01/12
  • CNEAI research evaluation. 01/01/06
Academic position: Prof. Titular Univ.
Email: jlgracia@unizar.es
ORCID number: 0000-0003-2538-9027

Research interests
  • Análisis numérico en ecuaciones en derivadas parciales
  • Álgebra lineal numérica
  • Análisis numérico en ecuaciones diferenciales ordinarias

PhDs
  • Doctor en Ciencias, sección Matemáticas, especialidad Matemática Aplicada. Universidad de Zaragoza. Universidad de Zaragoza. 1999

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An important part of my research has focused on the numerical approximation of singularly perturbed problems, which was the topic of my doctoral thesis that I defended in 1999. In this class of problems, some of the coefficients (singular perturbation parameter) can take arbitrarily small values, which causes its solution to have a multiscale character. In this area of research we have considered a wide range of problems, among which we can mention 2D problems of reaction-diffusion and convection-diffusion type, reaction-diffusion type systems coupled in the reaction terms, parabolic problems with discontinuities and incompatibilities and parabolic problems with attractive turning points. In all of them, the theoretical study of the asymptotic behavior of the solution and its derivatives with respect to the singular perturbation parameter was fundamental since it allowed us to construct uniformly convergent finite difference schemes.

Since 2012 I also became interested in the study of other types of integral-differential equations defined by derivatives of fractional order. These derivatives are being used in numerous applications that model complex processes or phenomena associated with non-local memory effects. In general, the solution of fractional order differential equations presents singularities and, therefore, specially designed numerical methods are also required to approximate their solution. To achieve this, it is crucial to have appropriate bounds of the derivatives of the solution that reveal its singularities. In our research we have considered problems with derivatives of fractional order in temporal or spatial variables.

In addition to the two areas mentioned above, I have also collaborated in other areas of research, such as, for example, in the Fourier analysis of multigrid methods and in the design of reduced order methods.

The results obtained in my research have been published in international journals. I currently have three research six-year terms, granted in the years 2006, 2012 and 2018. A total of 65 publications appear in the Thomson Reuters Web of Science, of which 48 are located in the first quartile of the category of research. Applied Mathematics. My H index is 18 and these works have been carried out in collaboration with 17 co-authors. An important part of my research has been in collaboration with foreign researchers, through numerous research visits. My total number of citations is 1342, of which 1241 are without own citations. The average number of appointments/year during the years 2018-2022 is 181.

The results have also been presented at national and international conferences. I have given 49 conferences and have collaborated in another 61 conferences. I have also been part of the Organizing Committee of international conferences held in Zaragoza (2010, 2012, 2019 and 2022) and Jaca (2018 and 2022). The latter have been organized in collaboration with the University Research Institute of Mathematics and Applications of the University of Zaragoza, of which I have been a member since 2007 and its secretary since February 2018. I was part of the Organizing Committee of the CEDYA/CMA 2022 Congress, which is the most relevant of Applied Mathematics at the national level, and attending more than 300 participants.

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