Search results for " partial differential equations"

showing 3 items of 43 documents

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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Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…

a priori error estimatesClass (set theory)Correctness010103 numerical & computational mathematics01 natural sciencesMeasure (mathematics)guaranteed and efficient a posteriori error boundsFOS: MathematicsApplied mathematicsPolygon meshMathematics - Numerical Analysis0101 mathematicserror indicators and adaptive mesh refinementMathematicsNumerical AnalysisApplied MathematicsRegular polygonNumerical Analysis (math.NA)convergence of finite element approximationsLipschitz continuity010101 applied mathematicsComputational MathematicsNonlinear systemexistence and uniqueness of solutionssemilinear partial differential equations65J15 49M29 65N15 65N30 65N50 35J20MathematikA priori and a posterioriPoisson-Boltzmann equationdifferentiaaliyhtälöt
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From Particle Systems to Partial Differential Equations International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019

2021

This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general…

interacting particle systems partial differential equations kinetic theory stochastic analysis modelling modelingSettore MAT/07 - Fisica Matematica
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