Search results for "Diffusion problem"
showing 7 items of 7 documents
Parallel Schwarz methods for convection-dominated semilinear diffusion problems
2002
AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.
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.
On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables
2021
In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
SPECIAL HPERBOLIC TYPE APPROXIMATION FOR SOLVING OF 3-D TWO LAYER STATIONARY DIFFUSION PROBLEM
2019
In this paper we examine the conservative averaging method (CAM) along the vertical z-coordinate for solving the 3-D boundary-value 2 layers diffusion problem. The special parabolic and hyperbolic type approximation (splines), that interpolate the middle integral values of piece-wise smooth function, is investigated. With the help of these splines the problems of mathematical physics in 3-D with respect to one coordinate are reduced to problems for system of equations in 2-D in every layer. This procedure allows reduce also the 2-D problem to a 1-D problem and the solution of the approximated problem can be obtained analytically. As the practical application of the created mathematical mode…
Functional A Posteriori Error Estimate for a Nonsymmetric Stationary Diffusion Problem
2015
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to an auxiliary function over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.
On mathematical modelling of the solid-liquid mixtures transport in porous axial-symmetrical container with Henry and Langmuir sorption kinetics
2018
In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs), one expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetical equation for absorption. The approximation of corresponding initial b…