6533b7d4fe1ef96bd1261e31

RESEARCH PRODUCT

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

Svetlana MatculevichMonika Wolfmayr

subject

Work (thermodynamics)Discretizationelliptic partial differential equations01 natural sciencesdiffuusiodiffuusio (fysikaaliset ilmiöt)mesh-adaptivityFOS: MathematicsNeumann boundary conditionApplied mathematicsBoundary value problemMathematics - Numerical Analysis0101 mathematicsDiffusion (business)virheanalyysiMathematicsosittaisdifferentiaaliyhtälötconvection-dominated diffusion problemsApplied Mathematicsta111010102 general mathematicsComputer Science - Numerical AnalysisNumerical Analysis (math.NA)a posteriori error estimation010101 applied mathematicsparabolic partial differential equationsComputational MathematicsElliptic partial differential equationA priori and a posterioriFokker–Planck equation

description

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.

yearjournalcountryeditionlanguage
2018-01-01
http://arxiv.org/abs/1803.09232