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We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The usual explicit finite-difference method of solving partial differential equations is limited in stability because it approximates the exact amplification factor by power-series. By adapting the same exponential-splitting method of…
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive…
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…
In this paper, diffusion in polymer solutions undergoing evaporation of solvent is modeled as a coupled heat and mass transfer problem with moving boundary condition within the framework of nonequilibrium thermodynamics. The proposed…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the…
We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of…