Related papers: A numerical scheme for a diffusion equation with n…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We introduce a new micro-macro decomposition of collisional kinetic equations in the specific case of the diffusion limit, which naturally incorporates the incoming boundary conditions. The idea is to write the distribution function $f$ in…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…