Numerical Analysis of PDE


The area of Numerical Analysis of Partial Differential Equations is involved in the development of methods and techniques for the solution of problems arising in science and engineering that can be described by means of PDE's.

The research field includes the development and analysis of numerical methods, stability and error analysis for finite element approximations, and its implementation for several applications in computational mechanics: structural vibration and acoustics, flui-structure interaction and slender structures, among others,

At the AM2V we also focus our research in the solution of control and optimization problems governed by PDE's. We are interested in analyzing, both theoretically and computationally, numerical methods and algorithms to solve optimal control problems by using finite element methods for the control as well as the state variables.

Members

  

Publications

  1. Hernández E, Kalise D, Braun P. Reduced-order LQG control of a Timoshenko beam model.. Bull Braz Math Soc. New Series 2016;47(1):143-155. [Bibtex]
  2. Hernández E, Cascón J. M, Engdahl A, Ferragut L. A reduced basis for a local high definition wind model. Computer Methods in Applied Mechanics and Engineering 2016;311:438-456. [Bibtex]
  3. Allendes A, Hernández E, Otárola E. A robust numerical method for a control problem of singularly perturbed equations. Computer and Mathematics with Applications. An International Journal 2016;72(4):974-991. [Bibtex]
  4. Allendes A, Durán F, Rankin R. Error estimation for low-order adaptive finite element approximations for some fluid flow problems. IMA Journal of Numerical Analysis 2016;36(4):1715-1747. [Bibtex]
  5. Porcu E, Ostoja-Starzewski M, Shen L. Harmonic oscillator driven by random processes having fractal and Hurst effects.. Acta Mechanica 2015;226(11):3653-3672. [Bibtex]
  6. Spa C, Hernández E, Anton R. A parallel GPU implementation of an explicit compact FDTD algorithm with a digital impedance filter for room acoustics applications.. IEEE/ACM Transactions on Audio, Speech, and Language Processing 2015;23(8):1368-1380. [Bibtex]
  7. Spa C, Hernández E, Caloen S. V. A Finite element approximations of a structural acoustic control problem with a Timoshenko beam interface. Journal of Mathematical Analysis and Applications 2015;424:1125-1142. [Bibtex]
  8. Spa C, Hernández E, Pedro R.-L. Numerical Absorbing Boundary Conditions Based on a Damped Wave Equation for Pseudo-Spectral Time-Domain Acoustic Simulations. The Scientific World Journal, 2014;2014(9):285945. [Bibtex]
  9. Ainsworth M, Allendes A, Barrenechea G. R, Rankin R. Fully computable a posteriori error bounds for stabilized FEM approximations of convection-reaction-diffusion problems in three dimensions. International Journal for Numerical Methods in Fluids 2013;73(9):765-790. [Bibtex]
  10. Ainsworth M, Allendes A, Barrenechea G. R, Rankin R. On the adaptive selection of the parameter in stabilized finite element approximations. SIAM Journal on Numerical Analysis 2013;51(3):1585-1609. [Bibtex]
  11. Escolano J, Spa C, Mateos T, Garriga A. Removal of afterglow effects in 2-D discrete-time room acoustics simulations. Applied Acoustics 2013;74(6):818-822. [Bibtex]
  12. Pozo L. P, Meneses R, Spa C, Durán O. A meshless FPM approximation for solving the RLW equation. Mathematical Problems in Engineering 2012;2012:22. [Bibtex]
  13. Garriga A, Spa C, Pérez L. Estudio Comparativo de Distintos Modelos de Condiciones de Contorno de Impedancia en problemas Acústicos. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 2012;28(4):214-224. [Bibtex]
  14. Hernández E, Barrios T, Bustinza R, García G. On Stabilized mixed methods for generalized Stokes problem based on the velocity-pseudostress formulation: A priori error estimates.. Computer Methods in Applied Mechanics and Engineering 2012;237–240:78-87. [Bibtex]
  15. Hernández E, Duarte S. Active control of sloshing in containers with elastic baffle plates. International Journal for Numerical Methods in Engineering 2012;91:604-621. [Bibtex]
  16. Allendes A, Ainsworth M, Barrenechea G, Rankin R. Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. IMA Journal of Numerical Analysis 2012;32(2):417-447. [Bibtex]
  17. Hernández E, Otárola E. A superconvergent scheme for a locking free FEM in a Timoshenko optimal control problem. Zamm-Z. Agnew. Math. Mech 2011;91(4):288-299. [Bibtex]
  18. Hernández E, Gamallo P, Peters A. On the error estimates for the finite element approximation of a class of boundary optimal control systems. Numerical Functional Analysis and Optimization 2011;32(4):383-396. [Bibtex]
  19. Spa C, Escolano J, Garriga A. Semi-empirical Boundary Conditions for the Linearized Acoustic Euler Equations using Pseudo-Spectral Time-Domain Methods. Applied Acoustics 2011;72(4):226-230. [Bibtex]
  20. Hernández E, Kalise D, Otárola E. A locking-free scheme for the LQR control of a Timoshenko beam. Journal on computational and Applied Mathematics 2011;(235):1383-1393. [Digital version] [Bibtex]
  21. Allendes A, Barrenechea G, Hernández E, Valentin F. A two-level Enriched finite element method for a mixed problem. Mathematics of Computation 2011;80(273):11-41. [Digital version] [Bibtex]
  22. Spa C, Escolano J, Garriga A, Mateos T. Compensation of the Afterglow Phenomenon in 2-D Discrete-Time Simulations. IEEE Signal Processing Letters 2010;17(8):758-761. [Digital version] [Bibtex]
  23. Spa C, Garriga A, Escolano J. Impedance Boundary Conditions for Pseudo-Spectral Time-Domain Methods in Room Acoustics. Applied Acoustics 2010;71:402-410. [Digital version] [Bibtex]
  24. Hernández E, Kalise D, Otárola E. Numerical approximation of the LQR problem in a strongly damped wave equation. Computational Optimization and Applications 2010;47:161-178. [Digital version] [Bibtex]
  25. Spa C, Mateos T, Garriga A. Methodology for Studying the Numerical Speed of Sound in Finite Differences Schemes. Acta Acustica United with Acustica 2009;95(4):690-695(6). [Digital version] [Bibtex]
  26. Zambra M, Fernández J, Hernández E, Pasten D, Muñoz V. Current Sheet Thickness in the Plasma Focus Snowplow Model. Journal of Plasma Fusion and Research Series 2009;8. [Digital version] [Bibtex]
  27. Hernández E, Otárola E, Rodríguez R, Sanhueza F. Approximation of the vibration modes of a Timoshenko curved rod of arbitrary geometry. IMA Journal of Numerical Analysis 2009;29:180-207. [Digital version] [Bibtex]
  28. Hernández E. Finite element approximation of the elasticity spectral problem on curved domains. Journal of Computational and Applied Mathematics 2009;225:452-458. [Digital version] [Bibtex]
  29. Hernández E, Hervella-Nieto L. Finite element approximation of free vibration of folded plates. Computer Methods in Applied Mechanics and Engineering 2009;98:1360-1367. [Digital version] [Bibtex]
  30. Hernández E, Otárola E. A locking free FEM in active vibration control of a Timoshenko beam. SIAM Journal on Numerical Analysis 2009;47(4):2432-2454. [Digital version] [Bibtex]
  31. Hernández E, Gamallo P. Error estimates for the approximation of a class of optimal control systems governed by linear PDEs. Numerical Functional Analysis and Optimization 2009;30(5):523 – 547. [Digital version] [Bibtex]
  32. Hernández E, Rodríguez R, Otárola E, Sanhueza F. Finite Element Approximation of the Vibration Problem for a Timoshenko Curved Rod. Revista de la Unión Argentina 2008;49:15-28. [Digital version] [Bibtex]
  33. Hernández E. Approximation of the vibration modes of plate and shells coupled with a fluid. Journal of Applied Mechanics, Trans. of the ASME 2006;73:1005-1010. [Digital version] [Bibtex]
  34. Hernández E, Rodríguez R. Finite Element approximation of spectral acoustic problems on curved domains. Numeritche Mathematik 2004;97:131-158. [Digital version] [Bibtex]
  35. Hernández E. Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements. ESAIM: M2AN (Mathematical Modelling and Numerical Analysis) 2004;38:1055-1070. [Digital version] [Bibtex]
  36. Hernández E, Rodríguez R. Finite Element approximation of spectral problems with Newman Boundary Conditions on Curved Domains. Mathematics of computation 2003;72:1099-1115. [Digital version] [Bibtex]
  37. Hernández E, Hervella-Nieto L, Rodríguez R. Computation of the vibration modes of plates and shells by low order MITC quadrilateral finite elements. Computers and structures 2003;81:615-628. [Digital version] [Bibtex]
  38. Hernández E, Hervella-Nieto L, Rodríguez R, Liberman E, Durán R. Error stimated for low order isoparametric quadrilateral finite elements for plates. SIAM Journal on Numerical Analysis 2003;41:1751-1752. [Digital version] [Bibtex]
  39. Hernández E, Hervella-Nieto L, Rodríguez R. Computation of the vibration modex of plates and shells coupled with a fluid. Computational machanics 2002;21:2453-2162. [Digital version] [Bibtex]
  40. Hernández E, Gatica G, Mellado M. A domain decomposition method for linear exterior boundary value problems. Applied Mathematical Letters 1998;11(6):1-9. [Digital version] [Bibtex]
  

Projects

  1. FONDECYT N°1140392: Numerical Methods for control problems and Applications
  2. Fondecyt No. 11121243: Fully computable a posteriori error estimation in finite element analysis
  3. Rise GEGAM Project. H2020 programme
  4. FONDECYT 3110046: A Finite Element Methods in the Time-Domain for Room Acoustics Applications
  5. Fondecyt Postdoctoral No3100072: Computational modeling of peristaltic pumping in 3D.

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