Perfil (CV) del personal docente investigador

Gracia Lozano, José Luis
Departamento: Departamento de Matemática Aplicada
Área: Matemática Aplicada
Centro: Escuela de Ingeniería y Arquitectura

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

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

Tramos de investigación
  • CNEAI research evaluation. 01/01/24
  • CNEAI research evaluation. 01/01/18
  • CNEAI research evaluation. 01/01/12
  • CNEAI research evaluation. 01/01/06
Categoría profesional: Prof. Titular Univ.

Cargos
  • Secretario del Instituto Universitario de Investigación de Matemáticas y Aplicaciones
Correo electrónico: jlgracia@unizar.es
ORCID: 0000-0003-2538-9027

Líneas de investigación
  • Análisis numérico en ecuaciones en derivadas parciales
  • Álgebra lineal numérica
  • Análisis numérico en ecuaciones diferenciales ordinarias

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

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Artículos

  • Gracia, José Luis; O’riordan, Eugene. Singularly perturbed elliptic problems of convection–diffusion type with non-smooth inflow/outflow boundary conditions. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2024. DOI: 10.1016/j.cam.2024.116094

  • Gracia, José Luis; Stynes, Martin. A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution. COMPUTATIONAL & APPLIED MATHEMATICS. 2024. DOI: 10.1007/s40314-024-02730-6

  • Solán-Fustero, P.; Gracia, J.L.; Navas-Montilla, A.; García-Navarro, P. Development of POD-based Reduced Order Models applied to shallow water equations using augmented Riemann solvers. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 2023. DOI: 10.1016/j.cma.2023.116038

  • Solán-Fustero, P.; Gracia, J. L.; Navas-Montilla, A.; García-Navarro, P. A POD-based reduced order model applied to 1D shallow water equations. IOP CONFERENCE SERIES: EARTH AND ENVIRONMENTAL SCIENCE. 2023. DOI: 10.1088/1755-1315/1136/1/012036

  • Gracia, J.L.; O'riordan, E. A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data. APPLIED NUMERICAL MATHEMATICS. 2023. DOI: 10.1016/j.apnum.2023.04.011

  • Solán-Fustero, P.; Gracia, J.L.; Navas-Montilla, A.; García-Navarro, P. A POD-based ROM strategy for the prediction in time of advection-dominated problems. JOURNAL OF COMPUTATIONAL PHYSICS. 2022. DOI: 10.1016/j.jcp.2022.111672

  • Gracia Lozano, J. L.; Navas-Montilla, A.; O''riordan, E. Parameter-uniform numerical methods for singularly perturbed linear transport problems. MATHEMATICAL METHODS IN THE APPLIED SCIENCES. 2022. DOI: 10.1002/mma.8446

  • Gracia, J.L.; O'riordan, E. Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition. APPLIED NUMERICAL MATHEMATICS. 2021. DOI: 10.1016/j.apnum.2020.12.013

  • Gracia, José Luis; Stynes, Martin. A finite difference method for an initial–boundary value problem with a Riemann–Liouville–Caputo spatial fractional derivative. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2021. DOI: 10.1016/j.cam.2020.113020

  • Gracia J.L.; O’riordan E. Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition. NUMERICAL ALGORITHMS. 2021. DOI: 10.1007/s11075-021-01098-6

  • Gracia, J.L.; O''riordan, E. Singularly perturbed reaction–diffusion problems with discontinuities in the initial and/or the boundary data. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2020. DOI: 10.1016/j.cam.2019.112638

  • Gracia, José Luis; O’riordan, Eugene; Stynes, Martin. Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann–Liouville–Caputo fractional derivative. BIT NUMERICAL MATHEMATICS. 2020. DOI: 10.1007/s10543-019-00777-0

  • Gracia, J.L.; O’riordan, E. Numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data in two space dimensions. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2020. DOI: 10.1007/978-3-030-41800-7_11

  • Clavero, C.; Gracia, J.L. Uniformly convergent additive schemes for 2d singularly perturbed parabolic systems of reaction-diffusion type. NUMERICAL ALGORITHMS. 2019. DOI: 10.1007/s11075-018-0518-y

  • Gracia, J.L.; O''riordan, E. Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data. APPLIED NUMERICAL MATHEMATICS. 2019. DOI: 10.1016/j.apnum.2019.08.005

  • Gracia Lozano, José Luis; O'riordan, Eugene; Stynes, Martin. A fitted scheme for a Caputo initial-boundary value problem. JOURNAL OF SCIENTIFIC COMPUTING. 2018. DOI: 10.1007/s10915-017-0631-4

  • Clavero, C.;Gracia, J.L. Efficient numerical methods for singularly perturbed systems of reaction-diffusion type. PUBLICACIONES DEL SEMINARIO MATEMÁTICO GARCÍA DE GALDEANO. 2018

  • Fernandez-Pato, J.; Gracia, J.L.; Garcia-Navarro, P. A fractional-order infiltration model to improve the simulation of rainfall/runoff in combination with a 2D shallow water model. JOURNAL OF HYDROINFORMATICS. 2018. DOI: 10.2166/hydro.2018.145

  • Gracia Lozano, José Luis; O'riordan, Eugene; Stynes, Martin. Convergence in positive time for a finite difference method applied to a fractional convection-diffusion equation. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. 2018. DOI: 10.1515/cmam-2017-0019

  • Stynes, M.; Gracia, J.L. Preprocessing schemes for fractional-derivative problems to improve their convergence rates. APPLIED MATHEMATICS LETTERS. 2017. DOI: 10.1016/j.aml.2017.05.016

  • Stynes, M.; O''riordan, E.; Gracia, J.L. Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. SIAM JOURNAL ON NUMERICAL ANALYSIS. 2017. DOI: 10.1137/16M1082329

  • Gracia, J.L.; O’riordan, E.; Stynes, M. Convergence outside the initial layer for a numerical method for the time-fractional heat equation. LECTURE NOTES IN COMPUTER SCIENCE. 2017. DOI: 10.1007/978-3-319-57099-0_8

  • Gracia, J. L.; O'riordan, E. A singularly perturbed convection–diffusion problem with a moving pulse. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2017. DOI: 10.1016/j.cam.2017.03.003

  • Gracia Lozano, José Luis; O'riordan, E. Singularly perturbed initial-boundary value problem with a pulse in the initial condition. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2017. DOI: 10.1007/978-3-319-67202-1_7

  • Clavero, C.; Gracia, J.L.; Shishkin, G. I.; Shishkina, L.P. An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2017. DOI: 10.1016/j.cam.2015.10.031

  • Gracia Lozano, José Luis; O'riordan, Eugene. Numerical approximation of solution derivatives of singularly peprturbed parabolic problems of convection-difffusion type. MATHEMATICS OF COMPUTATION. 2016. DOI: 10.1090/mcom/2998

  • Stynes, M.; O’riordan, E.; Gracia, J. L. Necessary conditions for convergence of difference schemes for fractional-derivative two-point boundary value problems. BIT NUMERICAL MATHEMATICS. 2016. DOI: 10.1007/s10543-016-0602-4

  • Gracia,J. L.; O'riordan,E. Numerical approximation of solution derivatives in the case of singularly perturbed time dependent reaction-diffusion problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2015. DOI: 10.1016/j.cam.2014.05.023

  • Gracia,J. L.; Stynes,M. Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2015. DOI: 10.1016/j.cam.2014.05.025

  • Gracia,J. L.; Oriordan,E. Scaled discrete derivatives of singularly perturbed elliptic problems. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. 2015. DOI: 10.1002/num.21900

  • Stynes, M.; Gracia, J.L. Boundary layers in a two-point boundary value problem with a caputo fractional derivative. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. 2015. DOI: 10.1515/cmam-2014-0024

  • Clavero, C.; Gracia, J. L.; Shishkin, G. I.; Shishkina, L. P. Schemes Convergent ¿-Uniformly for Parabolic Singularly Perturbed Problems with a Degenerating Convective Term and a Discontinuous Source. MATHEMATICAL MODELLING AND ANALYSIS. 2015. DOI: 10.3846/13926292.2015.1091041

  • Gracia Lozano, José Luis; Stynes, Martin. Formal consistency versus actual convergence rates of difference schemes for fractional-derivative boundary value problems. FRACTIONAL CALCULUS AND APPLIED ANALYSIS. 2015. DOI: 10.1515/fca-2015-0027

  • Clavero, C.; Gracia, J. L. An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems. APPLIED MATHEMATICS AND COMPUTATION. 2014. DOI: 10.1016/j.amc.2014.05.081

  • Shishkin, G.; Shishkina, L.; Gracia, J. L.; Clavero, C. On a numerical technique to study difference schemes for singularly perturbed parabolic reaction-diffusion equations. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. 2014

  • Gracia, J.L.; O'riordan, E. Interior layers in a singularly perturbed time dependent convection-diffusion problem. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. 2014

  • Gracia, José Luis; Stynes, Martin. A finite difference method for a two-point boundary value problem with a Caputo fractional derivative. IMA JOURNAL OF NUMERICAL ANALYSIS. 2014. DOI: 10.1093/imanum/dru011

  • Clavero, C.; Gracia, J. L. Uniformly convergent additive finite difference schemes for singularly perturbed parabolic reaction-diffusion systems. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2014. DOI: 10.1016/j.camwa.2013.12.009

  • Gracia,J. L.; O'riordan,E. A singularly perturbed reaction-diffusion problem with incompatible boundary-initial data. LECTURE NOTES IN COMPUTER SCIENCE. 2013. DOI: 10.1007/978-3-642-41515-9_33

  • Clavero, C.; Gracia, J.L. A high order uniformly convergent method with Richardson extrapolation in time for singularly perturbed reaction-diffusion parabolic problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2013. DOI: 10.1016/j.cam.2012.05.023

  • Clavero, C.; Gracia, J.L.; Shishkin, G.I.; Shishkina, L.P. Grid approximation of a singularly perturbed parabolic equation with degenerating convective term and discontinuous right-hand side. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. 2013

  • Gracia,J. L.;O'riordan,E. A singularly perturbed parabolic problem with a layer in the initial condition. APPLIED MATHEMATICS AND COMPUTATION. 2012. DOI: 10.1016/j.amc.2012.06.028

  • Clavero, C.;Gracia, J. L.;Shishkin, G.;Shishkina, L. Numerical experiments for a singularly perturbed parabolic problem with degenerating convective term and discontinuous source. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. 2012. DOI: 10.2478/cmam-2012-0014

  • Gracia,J. L.;O'riordan,E. A singularly perturbed convection-diffusion problem with a moving interior layer. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. 2012

  • Clavero,C.;Gracia,J. L. A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction-diffusion problems. APPLIED MATHEMATICS AND COMPUTATION. 2012. DOI: 10.1016/j.amc.2011.10.072

  • Clavero, C.; Gracia, J.L. Uniformly convergent finite difference schemes for singularly perturbed 1D parabolic reaction-diffusion problems. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2011. DOI: 10.1007/978-3-642-19665-2_9

  • Gracia, J.L.; O'riordan, E. A singularly perturbed convection diffusion parabolic problem with an interior layer. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2011. DOI: 10.1007/978-3-642-19665-2_15

  • Clavero,C.;Gracia,J. L.;Lisbona,F. Lecture Notes in Computational Science and Engineering: Preface. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2011. DOI: 10.1007/978-3-642-19665-2

  • Clavero,C.;Gracia, J.L. ;Stynes,M. A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2011. DOI: 10.1016/j.cam.2011.05.025

  • Gaspar, F.;Gracia, J. L.;Lisbona, F. J. ;Rodrigo, C. Efficient geometric multigrid implementation for triangular grids. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2010

  • Gaspar, F. J.;Lisbona, F. J.;Gracia, J. L. ;Rodrigo, C. Multigrid finite element methods on semi-structured triangular grids for planar elasticity. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. 2010

  • Gracia, J. L.;Lisbona, F. J. ;O'riordan, E. A coupled system of singularly perturbed parabolic reaction-diffusion equations. ADVANCES IN COMPUTATIONAL MATHEMATICS. 2010

  • Clavero, C.;Gracia, J. L. ;Lisbona, F. J. An almost third order finite difference scheme for singularly perturbed reactiondiffusion systems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2010

  • Clavero, C.;Gracia, J. L. ;Lisbona, F. Second order uniform approximations for the solution of time dependent singularly perturbed reaction-diffusion systems. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. 2010

  • Clavero, C.;Gracia, J. L. On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems. APPLIED MATHEMATICS AND COMPUTATION. 2010

  • Gaspar, F. J.; Gracia, J. L.; Lisbona, F. J.; Rodrigo, C. On Geometric Multigrid Methods for Triangular Grids using Three-Coarsening Strategy. APPLIED NUMERICAL MATHEMATICS. 2009. DOI: 10.1016/j.apnum.2009.01.003

  • Gaspar, F. J.;Gracia,J. L.;Lisbona,F. J. Fourier Analysis for Multigrid Methods on Triangular Grids. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2009

  • Clavero, Carmelo; Gracia Lozano, José Luis; Lisbona, Francisco. High order schemes for reaction-diffusion singularly perturbed systems. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2009. DOI: 10.1007/978-3-642-00605-0

  • Clavero, C.; Gracia, J.L.; Lisbona F.J. High order schemes for reaction-diffusion singularly perturbed systems. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2009

  • Gaspar, F. J.;Gracia,J. L.;Lisbona,F. J.;Osterlee,C. W. Distributive Smoothers in Multigrid for Problems with Dominating Grad-Div Operators. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. 2008

  • Gracia, J.L.; Lisbona, F.J.; Madaune-Tort, M.; O'riordan, E. A system of singularly perturbed semilinear equations. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2008. DOI: 10.1007/978-3-642-00605-0_12

  • Gaspar, F. J.;Gracia,J. L.;Lisbona,F. J.;Vabishchevich,P. N. A Stabilized Method for a Secondary Consolidation Biot's Model. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. 2008

  • Gracia, J. L.;Lisbona,F. J. A Uniformly Convergent Scheme for a System of Reaction-Diffusion Equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2007

  • Bujanda, B.;Clavero,C.;Gracia,J. L.;Jorge,J. C. A High Order Uniformly Convergent Alternating Direction Scheme for Time Dependent Reaction-Diffusion Singularly Perturbed Problems. NUMERISCHE MATHEMATIK. 2007

  • Gracia,J. L.;O'riordan,E.;Pickett,M. L. A parameter robust second order numerical method for a singularly perturbed two-parameter problem. APPLIED NUMERICAL MATHEMATICS. 2006

  • Gracia,J. L.;O'riordan,E. A defect-correction parameter-uniform numerical method for a singularly perturbed convection-diffusion problem in one dimension. NUMERICAL ALGORITHMS. 2006

  • Gracia,J. L.;Clavero,C. A compact finite difference scheme for 2D reaction-diffusion singularly perturbed problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2006

  • Clavero,C.;Gracia,J. L.;Jorge,J. C. A uniformly convergent alternating direction HODIE finite difference scheme for 2D time-dependent convection-diffusion problems. IMA JOURNAL OF NUMERICAL ANALYSIS. 2006

  • Clavero, C.; Gracia, J.L.; O'riordan, E. The defect-correction technique applied to singularly perturbed elliptic problems of convection-diffusion type. PUBLICACIONES DEL SEMINARIO MATEMÁTICO GARCÍA DE GALDEANO. 2006

  • Clavero, C.; Gracia, J.L.; Jorge, J-C. High-order numerical methods for one-dimensional parabolic singularly perturbed problems with regular layers. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. 2005

  • Clavero, C.;Gracia, J. L. High Order Methods for Elliptic and Time Dependent Reaction-Diffusion Singularly Perturbed Problems. APPLIED MATHEMATICS AND COMPUTATION. 2005

  • Clavero, C.;Gracia, J. L.;O'riordan, E. A Parameter Robust Numerical Method for a Two Dimensional Reaction-Diffusion Problem. MATHEMATICS OF COMPUTATION. 2005

  • Clavero, C.;Gracia, J. L. Hodie Finite Difference Schemes on Generalized Shishkin Meshes. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2004

  • Gracia, J.L; Clavero, C. Richardson extrapolation on generalized Shishkin meshes for singularly perturbed problems. PUBLICACIONES DEL SEMINARIO MATEMÁTICO GARCÍA DE GALDEANO. 2004

  • Gracia, J.L.; Jorge, J.C.; Bujanda B.; Clavero, C. High order uniformly convergent fractional step RK methods and HODIE finite difference schemes for 2D evolutionary convection-diffusion problems. JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING. 2003. DOI: 10.3233/JCM-2003-3304

  • Clavero, C.; Gracia, J.L. A HODIE method for 2D parabolic problems of convection-diffusion type. PUBLICACIONES DEL SEMINARIO MATEMÁTICO GARCÍA DE GALDEANO. 2003

  • Clavero, C. ; Gracia, J.L.; Lisbona, F. ;. Shishkin, G.I. A Robust Method of Improved Order for Convection-Diffusion Problems in a Domain with Characteristic Boundaries. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. 2002

  • Gracia, J.L.; Lisbona, F.; Clavero, C. High order epsilon-uniform methods for singularly perturbed reaction-diffusion problems. LECTURE NOTES IN COMPUTER SCIENCE. 2001. DOI: 10.1007/3-540-45262-1_41

  • Clavero, C.;Gracia, J. L.;Lisbona, F. High order methods on Shishkin meshes for singular perturbation problems of convection-diffusion type. NUMERICAL ALGORITHMS. 1999

Libros

Capítulos

  • José Luis Gracia, Eugene O'Riordan and Martin Stynes. A collocation method for a two-point boundary value problem with a Rienann-Liouville-Caputo fractional derivative. FIFTEENTH INTERNATIONAL CONFERENCE ZARAGOZA-PAU ON MATHEMATICS AND ITS APPLICATIONS: JACA (SPAIN), SEPTEMBER 10-12, 2018. 2019

  • An efficient numerical method for 2D systems of singularly perturbed parabolic reaction-diffusion equations. Clavero, Carmelo; Gracia Lozano, José Luis. PROCEEDINGS OF THE 17TH INTERNATIONAL CONFERENCE COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING. 2017

  • Aplicación de las derivadas fraccionarias a la simulación hidogeológica. Fernández-Pato, Javier; Gracia Lozano, José Luis; García-Navaro, Pilar. CMN 2017: CONGRESS ON NUMERICAL METHODS IN ENGINEERING. 2017

  • Applying a patched mesh method to efficiently solve a singularly perturbed reaction-diffusion problem. Gracia Lozano, José Luis; Madden, Niall; Nhan; Thái Anh MODELING, SIMULATION AND OPTIMIZATION OF COMPLEX PROCESS (HPSC, VIETNAN, 2015). 2017

  • A uniformly convergent method for a two parameter parabolic singularly perturbed problem with interior layers. Gracia Lozano, José Luis; Clavero, J. L. PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING. 2015

  • Blow-Up of Solutions and Interior Layers in a Caputo Two-Point Boundary Value Problem. Stynes, Martin; Gracia Lozano, José Luis LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING BOOK SERIES (PROCEEDINGS CONFERENCE BAIL 2014) 2015

  • Boundary Layers in a Riemann-Liouville Fractional Derivative Two-Point Boundary Value Problem. Gracia Lozano, José Luis; Stynes, Martin. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING BOOK SERIES (PROCEEDINGS CONFERENCE BAIL 2014) 2015

  • On the uniform convergence of singularly perturbed reaction-diffusion problems with non-smooth data. Gracia Lozano, José Luis. TWELFTH INTERNATIONAL CONFERENCE ZARAGOZA-PAU ON MATHEMATICS. 2014

  • A robust numerical method for a singularly perturbed parabolic convection-diffusion problem with a degenerating convective term and a discontinuous right-hand side. Clavero, C.; Gracia, J.L.; Shishkin, G.I.; Shishkina, L. NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS:PROCEEDINGS OF ENUMATH 201. 2013

  • Uniform convergence of the Crank-Nicolson and central differences scheme for 1D parabolic singularly perturbed reaction-diffusion problems. Clavero, C.; Gracia, J.L.; Lisbona, F.J. PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING. 2012

  • Development of efficient geometric multigrid algorithms by LFA for systems of partial differential equations on triangular grids. F.J.Gaspar ; J.L.Gracia ; F.J.Lisbona; C.Rodrigo. X INTERNATIONAL CONFERENCE ZARAGOZA-PAU OF APPLIED MATHEMATICS. 2010

  • A High Order HOC Finite Difference Schemes for 2D Reaction-Diffusion Singularly Perturbed Problems. Clavero, C.; Gracia, J.L. SPECIAL ISSUE ON COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING (CMMSE-2004). 2004

  • Richardson Extrapolation on Generalized Shishkin Meshes for Singularly Perturbed Problems. Clavero, C.; Gracia, J.L. VIII JOURNÉES ZARAGOZA-PAU DE MATHÉMATIQUES APPLIQUÉES ET DE STATISTIQUES. 2004

  • Splitting-time and exponential-fi tting-space discretizations for diffusion-reaction problems. Clavero, C:; Jorge, J.C.;Lisbona, F. PROCEEDINGS OF INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS, EQUADIFF 91. 1993

  • The Defect-Correction Technique Applied to Singularly Perturbed Elliptic Problems of Convection-Diffusion Type. Gracia Lozano, José Luis; Clavero Gracia, Carmelo. IX INTERNATIONAL CONFERENCE ZARAGOZA-PAU OF APPLIED MATHEMATICS.

Colaboraciones en ediciones de revista

  • International Journal of Numerical Analysis and Modeling. 1705-5105. 01/01/14 - 01/01/14

  • Abstract and Applied Analysis. 1085-3375. 24/07/12

  • Journal of Applied Mathematics. 1110-757X. 23/02/12

  • Lecture Notes in Computational Science and Engineering. 1439-7358. 01/01/11 - 01/01/11



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