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Publications by Pedro Díez

2019

A new 3D equilibrated residual method improving accuracy and efficiency of flux-free error estimates
Parés, N.; and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 120, pp. 391-432, 2019

Sampling-based stochastic analysis of the PKN model for hydraulic fracturing
Garikapati H., Verhoosel C. V., van Brummelen E. H., Zlotnik S. and Díez P.
Computational Geosciences, Vol. 23, pp. 81-105, 2019

2018

Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems
Garcia, R.; Diez, P.; Borzacchiello, D. and Chinesta, F.
Archives of Computational Methods in Engineering, Vol. 25, pp. 1003-1026, 2018

Algebraic PGD for tensor separation and compression: an algorithmic approach
Díez, P.; Zlotnik, S.; García-González, A.; Huerta, A.
Comptes rendus – Mécanique, Vol. 346, pp. 501-514, 2018

Numerical estimation of the bearing capacity of resistance spot welds in martensitic boron steels using a J-integral fracture criterion
Dorribo, D.; Greve, L.; Díez, P.; Arias, I.; Larrayoz-Izcara, X.
Theoretical and Applied Fracture Mechanics, Vol. 96, pp. 497-508, 2018

A non-intrusive proper generalized decomposition scheme with application in biomechanics
Zou, X.; Conti, M.; Díez, P. and Auricchio, F.
International Journal for Numerical Methods in Engineering, Vol. 113, pp. 230-251, 2018

Explicit parametric solutions of lattice structures with Proper Generalized Decomposition (PGD): Applications to the design of 3D-printed architectured materials
Sibileau, A.; García-González, A.; Auricchio, F.; Morganti, S. and Díez, P.
Computational Mechanics, Vol. 62, pp. 871-891, 2018

Numerical Modelling of Multi-Phase Multi-Component. Reactive Transport in the Earth’s interior
Oliveira, B. ; Afonso, J. C.; Zlotnik S. and Díez, P.
Geophysical Journal International, Vol. 212, Issue 1, pp. 345-388, 2018

2017

Generalized parametric solutions in Stokes flow
Díez, P., Zlotnik, S. and Huerta, A.
Computer Methods in Applied Mechanics and Engineering, Vol. 326, pp. 223-240, 2017

A semi-analytical scheme for highly oscillatory integrals over tetrahedra
Hospital-Bravo, R.; Sarrate, J. and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 111, Issue 8, pp. 703-723, 2017

Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment
García-Blanco, R.; Borzacchillelo, D.; Chinesta, F. and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 111, Issue 6, pp. 529-552, 2017

Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems
Serafin, K.; Magnain, B.; Florentin, E.; Parés, N. and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 110, Issue 5, pp. 440-466, 2017

Proper Generalized Decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems.
Signorini, M., Zlotnik, S. and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 109, Issue 8, pp. 1085-1102, 2017

A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates
N. Parés, N. and Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 313, Issue 1, pp. 785-816, 2017

2016

A reduced order modeling approach for optimal allocation of Distributed Generation in power distribution systems
García-Blanco, R.; Díez, P.; Borzacchiello, D. and Chinesta, F.
2016 IEEE International Energy Conference (ENERGYCON), Vol. , pp. 1-6, 2016

Unified formulation of a family of iterative solvers for power system analysis
Borzacchiello, D.; Chinesta, F.; Malik, M. H.; García-Blanco, R.; Diez, P.
Electric Power Systems Research, Vol. 140, pp. 201-208, 2016

Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment
Hospital-Bravo, R.; Sarrate, J. and Díez, P.
Computational Mechanics, Vol. 57, Issue 5, pp. 717-732, 2016

Adaptividade e Estimativas de Erro Orientadas por Metas Aplicadas a um Benchmark Test de Propagação de Onda
Steffens, L.M.; Díez, P.; Parés, N. and Alves, M.K.
Tendências em Matemática Aplicada e Computacional, Vol. 17, Issue 1, pp. 35-53, 2016

2015

An error estimator for real-time simulators based on model order reduction
Alfaro, I.; González, D.; Zlotnik, S.; Díez, P.; Cueto, E. and Chinesta, F.
Advanced Modeling and Simulation in Engineering Sciences, Vol. 2, Issue 1, pp. 1-30, 2015

Effect of the separated approximation of input data in the accuracy of the resulting PGD solution
Zlotnik, S.; Díez, P.; González, D,; Cueto, E. and Huerta, A.
Advanced Modeling and Simulation in Engineering Sciences, Vol. 2, Article number: 28, 2015

Un estimador de error residual semiexplícito en cantidades de interés para un problema mecánico lineal
Rosales, R. and Díez, P.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 32, Issue 4, pp. 212-220, 2015

Real time parameter identification and solution reconstruction from experimental data using the Proper Generalized Decomposition
Nadal, E., Chinesta, F., Díez, P., Fuenmayor, FJ. and Denia, FD
Computer Methods in Applied Mechanics and Engineering, Vol. 296, Issue 1, pp. 113-128, 2015

An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies
Afonso, JC, Zlotnik, S. and Díez, P.
Geochemistry, Geophysics, Geosystems, Vol. 16, Issue 10, pp. 3767-3777, 2015

Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields
Cottereau, R. and Díez, P.
Computational Mechanics, Vol. 56, Issue 4, pp. 601-612, 2015

Proper Generalized Decomposition of a geometrically parametrized heat problem with geophysical applications
S. Zlotnik, P. Díez, D. Modesto and A. Huerta
International Journal for Numerical Methods in Engineering, Vol. 103, Issue 10, pp. 737-758, 2015

A recovery-explicit error estimator in energy norm for linear elasticity
E. Nadal, P. Díez, J.J. Ródenas, M. Tur and F.J. Fuenmayor
Computer Methods in Applied Mechanics and Engineering, Vol. 287, pp. 172-190, 2015

2014

Goal-oriented space-time adaptivity for transient dynamics using a modal description of the adjoint solution
Verdugo, F.; Parés, N.; and Díez, P.
Computational Mechanics, Vol. 54, Issue 2, pp. 331-352, 2014

Error assessment in structural transient dynamics
Verdugo, F.; Parés, N.; and Díez, P.
Archives of Computational Methods in Engineering, Vol. 21, Issue 1, pp. 59-90, 2014

2013

Modal based goal-oriented error assessment for timeline-dependent quantities in transient dynamics
F. Verdugo, N. Parés and P. Díez
International Journal for Numerical Methods in Engineering, Vol. 95, Issue: 8, pp. 685-720, 2013

A stable XFEM formulation for multi-phase problems enforcing the accuracy of the fluxes through Lagrange multipliers
Díez, P.; Cottereau, R.; and Zlotnik, S.
International Journal for Numerical Methods in Engineering, Vol. 96, Issue 5, pp. 303-322, 2013

Meshless methods in dual analysis: theoretical and implementation issues
Ivannikov, V. ; Tiago, C.; Moitinho de Almeida, J.P. and Díez, P.
Engineering Analysis with Boundary Elements, Vol. 37, Issue 12, pp. 1728-1744, 2013

An algorithm for mesh refinement and un-refinement in fast transient dynamics
Casadei, F.; Díez, P., and Verdugo, F.
International Journal of Computational Methods, Vol. 10, Issue 4, pp. 1-31, 2013

SUPG-based stabilization of Proper Generalized Decompositions for the high-dimensional Advection-Diffusion Equations
Gonzalez, D.; Cueto, E.; Chinesta, F; Díez, P.; and Huerta, A.
International Journal for Numerical Methods in Engineering, Vol. 94, Issue: 13, pp. 1216-1232, 2013

Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation
Parés, N.; Díez, P. and Huerta, A.
International Journal for Numerical Methods in Engineering, Vol. 93, Num. 5, pp. 483-509, 2013

2012

Enforcing interface flux continuity in enhanced XFEM: stability analysis
Díez, P.; Zlotnik, S. and Cottereau, R.
Oberwolfach Reports, Vol. 9, Num: 1, pp. 523-526, 2012

Computable bounds of functional outputs in linear visco-elastodynamics
Verdugo, F. and Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 245-246, pp. 313-330, 2012

Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
Florentin, E. and Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 225, pp. 116-127, 2012

Modeling steel fiber reinforced concrete: numerical immersed boundary approach and a phenomenological mesomodel for concrete-fiber interaction
Pros, A.; Díez, P. and Molins, C.
International Journal for Numerical Methods in Engineering, Vol. 90, Issue 1, pp. 65-86, 2012

2011

Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
Steffens, L. M.; Parés, N. and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 86 Issue 10, pp. 1197-1224, 2011

Numerical modeling of the Double Punch Test for plain concrete
Pros, A.; Díez, P. and Molins, C.
International Journal of Solids and Structures, Vol. 48, Issues 7-8, pp. 1229-1238, 2011

Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies
Steffens, L. M.; Parés, N. and Díez, P.
Computational Mechanics, Vol. 47 Number 6, pp. 681-699, 2011

Numerical modeling of erosion using an improvement of the extended finite element method
Cottereau, R and Díez, P
European Journal of Environmental and Civil Engineering, Vol. 15, pp. 1187-1206, 2011

2010

Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method
Cottereau, R., Chamoin, L. and Díez, P.
Mécanique & Industries, Vol. 11 Number 3-4, pp. 249-254, 2010

Error Estimation and Quality Control
Diez, P.; Parés, N. and Huerta, A.
Encyclopedia of Aerospace Engineering, Wiley, Vol. 3, Part 15, Chapter 144, pp. 1725-1734, 2010

XFEM+: una modificación de XFEM para mejorar la precisión de los flujos locales en problemas de difusión con conductividades muy distintas
Cordero, F. and Díez, P.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 26, Issue 2, pp. 121-133, 2010

A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation
Larsson, F; Díez, P and Huerta, A.
Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2383-2402, 2010

Modeling, with a unified level-set representation, of the expansion of a hollow in the ground under different physical phenomena
Cottereau, R; Díez, P and Huerta, A
Computational Mechanics, Vol. 42, Issue 2, pp. 315-327, 2010

An error estimator for separated representations of highly multidimensional models
Ammar A; Chinesta F; Díez, P and Huerta, A
Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issues 25-28, pp. 1872-1880, 2010

Accurate recovery-based upper error bounds for the extended finite element framework
Ródenas, J.J.; González-Estrada, O.A.; Díez, P. and Fuenmayor, F.J.
Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2607-2621, 2010

SUPG-based stabilization using a separated representations approach
González, D.; Debeugny, L.; Cueto, E.; Chinesta, F.; Díez, P. and Huerta, A.
International Journal of Material Forming, Vol. 3, pp. 883-886, 2010

Error assessment and mesh adaptivity for regularized continuous failure models
Pannachet, T; Díez, P; Askes, H and Sluys, L. J.
Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issues 17-20, pp. 961-978, 2010

Assembling sparse matrices in MATLAB
Zlotnik, S. and Díez, P.
Communications in Numerical Methods in Engineering, Vol. 26, Issue 6, pp. 760-769, 2010

2009

Guaranteed energy error bounds for the Poisson equation using a flux-free approach: solving the local problems in subdomains
Parés, N., Santos, H., and Díez, P.
International Journal for Numerical Methods in Engineering, Vol. 79, Issue 10, pp. 1203-1244, 2009

Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates
Parés, N., Díez, P., Huerta, A.
Journal on Scientific Computing (SIAM), Vol. 31, Issue 4, pp. 3064-3089, 2009

Hierarchical X-FEM for n-phase flow (n>2)
Zlotnik, S., Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 198 Issues 30-32, pp. 2329-2338, 2009

Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method
Cottereau, R; Díez, P and Huerta, A
Computational Mechanics, Vol. 44, Issue 4, pp. 533-547, 2009

A simple strategy to assess the error in the numerical wave number of the Finite Element solution of the Helmholtz equation
Steffens, L.M.,Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issues 15-16, pp. 1389-1400, 2009

Estima de error residual explícita para cantidades de interés utilizando funciones burbuja
Rosales, R. and Díez, P.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 25, Issue 4, pp. 337-357, 2009

2008

Bounds for quantities of interest and adaptivity in the Element Free Galerkin method
Vidal, Y., Parés, N., Díez, P., Huerta, A.
International Journal for Numerical Methods in Engineering, Vol. 76, Issue 11, pp. 1782-1818, 2008

Small-scale gravitational instabilities under the oceans: implications for the evolution of oceanic lithosphere and its expression in geophysical observables
Zlotnik, S., Afonso, J.C., Díez, P, and Fernández, M.
Philosophical Magazine, Vol. 88, Issues 28-29, pp. 3197-3217, 2008

Modelling Gravitational Instabilities: Slab Break-off and Rayleigh-Taylor Diapirism
Zlotnik, S., Fernández, M., Díez, P. and Vergés, J.
Pure and Applied Geophysics, Vol. 165, Issue 8, pp. 1491-1510, 2008

Bounds of functional outputs for parabolic problems. Part I: Exact bounds of the Discontinuous Galerkin time discretization
Parés, N., Díez, P. and Huerta, A..
Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issues 19-20, pp. 1641-1660, 2008

Bounds of functional outputs for parabolic problems. Part II: Bounds of the exact solution
Parés, N., Díez, P. and Huerta, A..
Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issues 19-20, pp. 1661-1679, 2008

2007

Numerical Modelling of Tectonic Plates Subduction using X-FEM
Zlotnik, S., Díez, P., Fernández, M. and Vergés, J.
Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issues 41-44, pp. 4283-4293, 2007

Equilibrated Patch Recovery error estimates: simple and accurate upper bounds of the error
Diez, P., Rodenas, J.J. and Zienkiewicz, O.C.
International Journal for Numerical Methods in Engineering, Vol. 69, Issue 10, pp. 2075-2098, 2007

Goal-oriented error estimation for transient parabolic problems
Pedro Díez, Giovanni Calderón
Computational Mechanics, Vol. 39, Issue 5, pp. 631-646, 2007

Remeshing criteria and proper error representations for goal oriented h-adaptivity
Díez, P. and Calderon, G.
Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4, pp. 719-733, 2007

2006

Análisis de diferentes estimadores de error de postproceso para adaptatividad orientada al resultado
Giovanni Calderón y Pedro Díez
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 22 Issue 2, pp. 193-213, 2006

Preface
N.-E. Wiberg and P. Díez
Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issues 4-6, pp. 205-206, 2006

Subdomain-based flux-free a posteriori error estimators
Núria Parés, Pedro Díez and Antonio Huerta
Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issues 4-6, pp. 297-323, 2006

2004

Accurate upper and lower error bounds by solving flux-free local problems in “stars”
Díez, P., Parés, N. y Huerta, A.
European Journal of Finite Elements (Revue Européenne des éléments finis), Vol. 13, Issue 5-6-7/2004, pp. 497-507, 2004

2003

Convergence of finite elements enriched with meshless methods
Fernández-Méndez, S., Díez, P. and Huerta, A.
Numerische Mathematik, Vol. 96, Issue 1, pp. 43-59, 2003

A note on the convergence of the secant method for simple and multiple roots
Pedro Díez
Applied Mathematics Letters, Vol. 16, Issue 8, pp. 1211-1215, 2003

Goal-oriented adaptivity for shell structures: Error assessment and remeshig criteria
Díez, P., Morata, I. and Huerta A.
European Journal of Finite Elements (Revue Européenne des éléments finis), Vol. 12, Issue 6, pp. 691-715, 2003

Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates
Díez, P., Parés; N. And Huerta,A.
International Journal for Numerical Methods in Engineering, Vol. 56, Issue 10, pp. 1465-1488, 2003

2002

Enrichissement des interpolations d’éléments finis en utilisant des méthodes de particules
Huerta, A., Fernández-Méndez, S. and Díez, P.
Mathematical Modelling and Numerical Analysis, Vol. 36, Issue 6, pp. 1027-1042, 2002

Error estimation and adaptivity for nonlinear FE analysis
Antonio Huerta, Antonio Rodríguez-Ferran and Pedro Díez
International Journal of Applied Mathematics and Computer Sciences, Vol. 12, Issue 1, pp. 59-70, 2002

2001

Probabilistic analysis of an a posteriori error estimator for finite elements
Díez, P. and Egozcue, J.J.
Mathematical Models and Methods in Applied Sciences, Vol. 11, Issue 5, pp. 841-854, 2001

2000

Adaptivity based on error estimation for viscoplastic softening materials
Díez, P., Arroyo, M. and Huerta, A.
Mechanics of Cohesive-Frictional Materials, Vol. 5, Issue 2, pp. 87-112, 2000

Error Estimation Including Pollution Assessment for Nonlinear Finite Element Analysis
Huerta, A. and Díez, P.
Computer Methods in Applied Mechanics and Engineering, Vol. 181, Issues 1,3, pp. 21-41, 2000

Error estimation for adaptive computations on shell structures
Díez, P., and Huerta, A.
European Journal of Finite Elements (Revue Européenne des éléments finis), Vol. 9, Issue 1, 2 i 3,/2000, pp. 49-66, 2000

1999

Adaptive finite element strategies based on error assessment
Huerta, A., Rodríguez-Ferran, A., Díez, P. and Sarrate, J.
International Journal for Numerical Methods in Engineering, Vol. 46, Issue 10, pp. 1803-1818, 1999

A unified approach to remeshing strategies for finite element h-adaptivity
Díez, P. and Huerta, A.
Computer Methods in Applied Mechanics and Engineering, Vol. 176, Issues 1, 4, pp. 215-229, 1999

1998

A posteriori error estimation for standard finite element analysis
Díez, P., Egozcue, J.J. and Huerta, A.
Computer Methods in Applied Mechanics and Engineering, Vol. 163, Issues 1,4, pp. 141-157, 1998

Un estimador de error residual para el método de los elementos finitos
Díez, P., Egozcue, J.J. and Huerta, A.
Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 14, Issue 4, pp. 557-582, 1998

1997

Vulnerabilidad sísmica y toma de decisiones
Egozcue, J.J., Simarro, G. and Díez, P.
Revista Internacional de Cálculo de Estructuras, Vol. 174, pp. 35-58, 1997