Related papers: Two-scale numerical simulation of the weakly compr…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying…
In astrophysics and meteorology there exist numerous situations where flows exhibit small velocities compared to the sound speed. To overcome the stringent timestep restrictions posed by the predominantly used explicit methods for…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume…
In this paper we continue the analysis of the two-scale method for the Monge-Amp\`ere equation for dimension $d \geq 2$ introduced in [10]. We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary…
We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and…
We present a numerical approximation of the solutions of the Euler equations with a gravitational source term. On the basis of a Suliciu type relaxation model with two relaxation speeds, we construct an approximate Riemann solver, which is…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Finite volume schemes often have difficulties to resolve the low Mach number (incompressible) limit of the Euler equations. Incompressibility is only non-trivial in multiple spatial dimensions. Low Mach fixes, however generally are applied…
In this article our goal is to study the singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $=\epsilon^m $, Rossby number $=\epsilon $ and Froude number $=\epsilon^n…
We adapt the concept of $\mathcal{K}-$convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions…
This paper is devoted to numerical simulation of a charged particle beam submitted to a strong oscillating electric field. For that, we consider a two-scale numerical approach as follows: we first recall the two-scale model which is…
The authors propose and analyze a well-posed numerical scheme for a type of ill-posed elliptic Cauchy problem by using a constrained minimization approach combined with the weak Galerkin finite element method. The resulting Euler-Lagrange…
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on the space of square-integrable functions, whose…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in [1, 3] with the constraint introduced into the system by a singular pressure law, which causes the transition of…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…