Semi-lagrangian (or remeshed) particle methods are conservative particle methods where the particles are remeshed at each time-step. The numerical analysis of these methods show that their accuracy is governed by the regularity and moment properties of the remeshing kernel and that their stability is guaranteed by a lagrangian condition which does not rely on the grid size. Turbulent transport ...

The subject of this paper is the investigation of the Magnus expansion of a solution of the linear diierential equation y 0 = a(t)y, y(0) 2 G, where G is a Lie group and a : R + ! g, g being the Lie algebra of G. We commence with a brief survey of recent work in this area. Next, building on earlier work of Iserles and NNrsett, we prove that an appropriate truncation of the expansion is time-sym...

In the fourth installment of the celebrated series of five papers entitled “Towards the ultimate conservative difference scheme”, Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a ...

In this talk, we devise a new Runge-Kutta Discontinuous Galerkin (RKDG) method that achieves full high-order convergence in time and space while keeping the timestep proportional to the spatial mesh-size. To this end, we derive an extension to non-autonomous linear systems of the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme with low storage described in Gottlieb et...

Abstract In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for third derivatives in truncation error remainder, two high-order compact LOD schemes are established solving two- three- dimensional advection equations, respectively. They have fourth-order accuracy both time space. By von Neumann analysis it shows that unconditionally stable. Bes...

We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The VEF discretizations are coupled a Discontinuous Galerkin (DG) of discrete ordinates transport equation form effective linear algorithms that compatible with (curved) meshes. This combination is mo...

In this paper, an epidemic model with spatial dependence is studied and results regarding its stability numerical approximation are presented. We consider a generalization of the original Kermack McKendrick in which size populations differs space. The use local yields system partial-differential equations integral terms. uniqueness qualitative properties continuous analyzed. Furthermore, differ...