The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov–Poisson equation. Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes. In this paper we study the conservation of important invari...

This paper is devoted to the autonomous Lagrange problem of the calculus of variations with a discontinuous Lagrangian. We prove that every minimizer is Lipschitz continuous if the Lagrangian is coercive and locally bounded. The main difference with respect to the previous works in the literature is that we do not assume that the Lagrangian is convex in the velocity. We also show that, under so...

[1] Motivated by increases in the realism of OGCMs and the number of drifting buoys in the ocean observing system, a new Lagrangian assimilation technique is implemented in an idealized, reduced-gravity configuration of the layered primitive equation model MICOM. Using an extensive set of twin experiments, the effectiveness of the Lagrangian observation operator and of a dynamical balancing tec...

Wave-mean flow equations for mass and momentum conservation in three dimensions, previously obtained with a vertical coordinate transform, are generalized here to random waves, and re-derived from the Generalized Lagrangian Mean equations. Combining the momentum equation with a three-dimensional equation for wave pseudo-momentum yields a set of equations describing the interactions of waves, me...

Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method developed in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved o...

We develop an Eulerian-Lagrangian iterative solution technique for accurate and efficient numerical simulation of single-phase compositional flow through three-dimensional compressible porous media in the presence of multiple injection and production wells. In the numerical simulator, an Eulerian-Lagrangian method is used to solve the convectiondiffusion transport equations and a mixed finite e...

relativistic cosmology Hideki Asada∗ and Masumi Kasai† Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan (April 2, 1999) We develop the Lagrangian perturbation theory in the general relativistic cosmology, which enables us to take into account the vortical effect of the dust matter. Under the Lagrangian representation of the fluid flow, the propagation equation fo...

An equation describing particles with spin 3/2 is derived. This equation can be considered as " square root " of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The equation considered involves fields with spin-3/2 and spin-1/2 (one copy), i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and...

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE approach, the surface tension, which may be a li...

3 Anatoly Abrashkin and Efim Pelinovsky 4 5 a National Research University Higher School of Economics (HSE), Nizhny Novgorod 6 603155, Russia 7 b Institute of Applied Physics, 603950, 46 Ulyanov str., Nizhny Novgorod, Russia 8 c Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia 9 10 11 Abstract: 12 The nonlinear Schrödinger equation (NLS equation) describing weakly 13 rotation...