Related papers: Perfect absorption in Schr\"odinger-like problems …
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…
We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schr\"odinger--KdV system on a bounded domain. This system models the interaction of short and long waves. Since the energy…
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schr\"odinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a…
We present a set of smooth infinite energy global solutions (without spatial symmetry) to the non-integrable, nonlinear Schr\"odinger equations on $\Bbb R$. These solutions are space-time quasi-periodic with two frequencies each. Previous…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We show the sharp global well posedness for the Cauchy problem for the cubic (quartic) non-elliptic derivative Schr\"odinger equations with small rough data in modulation spaces $M^s_{2,1}(\mathbb{R}^n)$ for $n\ge 3$ ($n= 2$). In 2D cubic…
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…
Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when continuous Lagrange finite element spaces of odd polynomial…
We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This…