On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
This work provides computable error bounds for a specific class of PDEs, which is incremental for researchers in computational neuroscience and numerical analysis.
The authors derive reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem in computational neuroscience, covering static and time-dependent cases with different boundary conditions. Numerical examples confirm the reliability and efficiency of the estimates.
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.