245 citations · 424 across the 13 of their papers we have counts for
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Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson--Nernst--Planck/Navier--Stokes equations
Mehdi Dehghan, Zeinab Gharibi, Ricardo Ruiz-Baier
In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson-Nernst-Planck (PNP) and Navier--S…
Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion models
Mostafa Abbaszadeh, Amirreza Khodadadian, Mehdi Dehghan +1
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are…
Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphere
Vahid Mohammadi, Mehdi Dehghan, Amirreza Khodadadian +1
In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique,…
Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
Hamid Moghaderi, Mehdi Dehghan, Marco Donatelli +1
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and comp…
A numerical method based on the reproducing kernel Hilbert space method for the solution of fifth-order boundary-value problems
Mustafa Inc, Ali Akgül, Mehdi Dehghan
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM)…