Space-Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
25/2007
Title:
Space-Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes
Date:
Monday 10th December 2007
Author(s):
Micheletti, Stefano; Perotto, Simona
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Abstract:
We deal with the approximation of an unsteady advection-diffusion-
reaction problem by means of space-time finite elements, continuous affine
in space and piecewise constant in time. In particular, we are interested in
the advection-dominated framework. To face the trade-off between
computational cost and accuracy, we devise a space-time adaptive procedure
where both the time step and the spatial grid are adapted throughout the
simulation. Two are the key points involved: the derivation of an a
posteriori error estimator where the contributions of the spatial and of the
temporal discretization are split; a balance of these two contributions via a
proper adaptive scheme. The main novelty of the paper is the interest for
an anisotropic mesh adaption framework.