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]
  

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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