Space–Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes

S. Micheletti () and S. Perotto ()
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S. Micheletti: Politecnico di Milano, MOX, Dipartimento di Matematica “F. Brioschi”
S. Perotto: Politecnico di Milano, MOX, Dipartimento di Matematica “F. Brioschi”

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 49-56 from Springer

Abstract: 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.

Keywords: Posteriori Error; Adaptive Algorithm; Parabolic Problem; Posteriori Error Estimate; Posteriori Error Estimator (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_5

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