Estimation of error a posteriori for the transport equation of CO2 in a pulmonary alveolus with the finite element method

Authors

  • Obidio Rubio
  • Luis Caucha
  • Alexis Rodríguez
  • Robert Haro

DOI:

https://doi.org/10.17268/sel.mat.2017.01.10

Keywords:

FEMdG (r), posterior error, CO2 transport, variational formulation

Abstract

In this paper we present an estimate of the posterior error of finite element-constructed finite element meshes and finite element discontinuous over time for the transport equation of CO2 in the bags Alveolar cells of the human lung, using the dual weighted residual method (DWR).

References

A. Chorin and J. Marsden, Introduction to Fluid Mechanics. Sprienger-Verlag, New York, 1979.

R. Becker and R. Rannacher, Weighted a-posteriori error estimates in FE methods, Lecture ENUMATH95, Paris, Sept. 18-22, 1995, in: Proc. ENUMATH-97, Heidelberg, Sept. 28 - Oct.3, 1997 (H.G. Bock, et al., eds), pp. 621-637, World Scientific Publ., Singapore, 1998.

R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: Basic analysis and examples, East-West J. Numer. Math., 4:237-264 (1996).

R. Becker and R. Rannacher, An optimal control approach to error estimation and mesh adaptation in finite element methods, Acta Numerica 2000 (A. Iserles, ed.), pp. 1-102, Cambridge University Press, 2001.

R. Becker, V. Heuveline, and R. Rannacher, An optimal control approach to adaptivity in computational fluid mechanics, Int. J. Numer. Meth. Fluids. 40, 105-120 (2002).

W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations, Lectures in Mathematics, ETH Zurich, Birkhauser, Basel 2003.

R. Becker, An Adaptive Finite Element Method for the Incompress- ible Navier-Stokes Equations on TimeDependent Domains, Doctor Thesis, Preprint 95-44, SFB 359, Nov. 1995, University of Heidelberg.

R. Becker, Weighted error estimators for finite element approximations of the incompressible Navier-Stokes equations, Preprint 98-20, SFB 359, Uni- versity of Heidelberg, submitted for publication, 1998.

R. Becker, R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numerica, Cambridge University Press, pp. 1-102, (2001).

L. Caucha, A. Rodriguez, O. Rubio, Existence and uniqueness of solutions to a model for dynamic of CO2 in the alveolar sac of human lung, sometido a Nonlinerar Analysis, 2016.

M. Cotrina, L. Lara, O. Rubio, Elemento Finito Adaptativo en la solución de la Ecuación de Poisson con coeficientes discontinuos, Selecciones Matemáticas, Vol. 1 No. 2 , 2015, pp 1- 19.

K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Introduction to adaptive methods for differential equations, Acta Numerica 1995 (A. Iserles, ed.), pp. 105-158, Cambridge University Press.

P. Houston, R. Rannacher and E.Suli, A posteriori error analysis for stabilised finite element approximations of transport problems, Comput. Methods Appl. Mech. Enrg. 190 (2000), 1483-1508.

Rof Rannacher, On the adaptive discretization of PDE-based optimization problems, lecture given at the Summer School PDE Constrained Optimization in Tomar, Portugal, July 27-29, 2005.

R. Reupo, Existencia y Unicidad de la solución del sistema de ecuaciones que modelan el flujo de aire y su interacción con el alveolo pulmonar, thesis doctoral , por someter a la Universidad Nacional de Trujillo, 2017, presentada Escuela de Postgrado, UNT.

Published

2017-07-13

How to Cite

Rubio, O., Caucha, L., Rodríguez, A., & Haro, R. (2017). Estimation of error a posteriori for the transport equation of CO2 in a pulmonary alveolus with the finite element method. Selecciones Matemáticas, 4(01), 102-111. https://doi.org/10.17268/sel.mat.2017.01.10

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