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Luca Ferracina
| Speaker: |
Dr. Luca Ferracina (CWI, Amsterdam)
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| Date: |
Friday June 1, 2007
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| Title: |
An adaptive
finite element method of lines approach for coupled reaction-diffusion
equations in Ω-δΩ
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Abstract
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A
numerical study of an Adaptive Finite Element Method Of Lines (AFEMOL)
approach is presented for the approximation of the solution of a system
of reaction-diffusion equations coupling species defined on a
2-dimensional domain and species confined to the boundary of the
domain. In order to bound the energy norm of the space discretization
error, in the AFEMOL the spatial mesh changes automatically at selected
times when the underlying triangulation is refined in areas where it is
needed. The decision of when and where to modify the mesh is based on
the estimation of the space discretization error.
The adaptive process and the a-posteriori explicit error estimation
exploited in this talk are a modification of the pioneer work developed
by Bieterman and Babuška in [Numer. Math. 40 (1982), 339], [Numer.
Math. 40 (1982), 373], [J. Comput. Phys. 63 (1986), 33]. The primary
interest is the effect of the coupling Ω-δΩ on the performance of the
error estimator and the successive adaptive process.
Our numerical results indicate that the global error estimators are
accurate, the local error indicators are reliable and that the adaptive
strategy successfully controls the space discretization error.
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