On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems

On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and tim...

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Bibliographic Details
Main Authors: Matculevich, Svetlana, Wolfmayr, Monika
Format: Journal Article
Language:English
Published: 25-03-2018
Subjects:
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Online Access:Get full text
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Summary:This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
DOI:10.48550/arxiv.1803.09232