Search results for "convection-dominated diffusion problems"

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

2018

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.

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
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