This paper is devoted to comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is ut þ ðu uÞx 1⁄4 ðuuxxxÞx, which arises in the context of thin film flow. First we employ implicit schemes and treat both convection and diffusion terms implicitly. Then the convection terms are treated with wellknown explicit schemes, namely Godunov,...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

Recently many mathematical models for image processing have been widely applied in computer visualization. The nonlinear diffusion PDE has been broadly applied in image processing. In this paper we propose a convection-diffusion filter by adding a convection term in the modified diffusion equation as a physical interpretation for removing the noise. We study the dynamics of such equations by th...

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that robust also the convection dominated regime. For original method introduced [Benedetto et al. , CMAME 2016] we are able show an “almost uniform” error bound (in sense unique term depends unfavourable way on parameters damped by higher order me...