We develop and analyze methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes. The methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes. The novel aspect of the scheme is the construction of a linear approximatio...

Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employe...

Spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for Computational Fluid Dynamics (CFD). Mesh skewness is then typically encountered causing severe deterioration of the formal order of accuracy of the discretisation, or boundedness of the solution, or both. Particularly methods inherently relying on the accurate and boun...

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection...

Abstract. We consider the problem of optimal mixing control. Our objective is to best enhance mixing by flow advection while the flow is optimized in the sense that it is almost steady and is of the least magnitude and the least rotation. For this we define a mixing efficiency functional by penalizing the average of variance of a diffusive scalar, the average of the flow, and the average of its...

An algorithm based on operator splitting has been successfully implemented for solving unsteady, advectiondominated transport problems in 3-D. Specifically, the general operator-integration-factor splitting method of Maday et al. is applied to the unsteady advection–diffusion equation with source/sink terms. The algorithm incorporates a 3-D characteristic Galerkin scheme to treat advection, and...

A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpola...

This article explores the heat and mass transfer behaviour of magnetohydrodynamic free convective flow past a permeable vertical rotating cone and a plate filled with gyrotactic microorganisms in the presence of nonlinear thermal radiation, thermo diffusion and diffusion thermo effects. We presented dual solutions for the flow over a rotating cone and a rotating flat plate cases. Similarity var...

in this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. the governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by sherief et al. [1] are considered as a special case. it is found that three types of...