This note recounts detailed stability and accuracy analysis of a scalar advection-diffusion equation.

A finite volume algorithm for the solution of the reaction–advection–diffusion equation on the sphere is derived and evaluated using analytical solutions. The proposed approach is based on the principle of semidiscretization. The convective and diffusive fluxes are approximated first, and then the resulting set of the ordinary differential equations (ODEs) is solved using the appropriate time s...

In this paper we investigate the numerical approximation of fractional diffusion, advection, reaction equation on a bounded interval. Recently explicit form solution to was obtained. Using boundary behavior and Jacobi polynomials, Petrov–Galerkin scheme is proposed analyzed. Numerical experiments are presented which support theoretical results, demonstrate accuracy optimal convergence method.

We present a theoretical study of nonlinear pattern selection mechanisms in a model of bounded reaction-diffusion-advection system. The model describes the activator-inhibitor type dynamics of a membrane reactor characterized by a differential advection and a single diffusion; the latter excludes any finite wave number instability in the absence of advection. The focus is on three types of diff...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 31 March 2021Accepted: 07 September 2021Published online: 02 December 2021Keywordsreaction-diffusion-advection systems, nonsmooth diffusion coefficients, mass control, global existence, $L^p$-energy methodsAMS Subject Headings35A01, 35K57, 35K58, 35Q92Publication DataISSN...

This study investigates the viscous term formulation for the newly developed energy stable flux reconstruction (ESFR) scheme, as an extension to the linear advection flux formulation in the original ESFR scheme. The concept of energy stability for the flux reconstruction approach is put forward. This paper also discusses the formulation of inviscid first derivative flux based on flux reconstruc...