Related papers: Numerical approximations to a singularly perturbed…
We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
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…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
For singularly perturbed convection-diffusion problems, supercloseness analysis of finite element method is still open on Bakhvalov-type meshes, especially in the case of 2D. The difficulties arise from the width of the mesh in the layer…
The cutoff method, which cuts off the values of a function less than a given number, is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations. A convergence analysis is given for a broad…
We consider the third-order wide-angle `parabolic' equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range-dependent bathymetry. It is known that the initial-boundary-value problem for this equation…
We study an initial boundary value problem for a cross-diffusion system in population dynamics. The mathematical challenge is due to the fact that the determinant of the coefficient matrix of the system changes signs. As a result, the…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
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…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear convection-diffusion systems. The upwind-biased flux with adjustable numerical…