Related papers: Stability of finite difference schemes for the hyp…
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the…
Modern shock-capturing schemes often suffer from numerical shock anomalies if the flow field contains strong shocks, which may limit their further application in hypersonic flow computations. In the current study, we devote our efforts to…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…
In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the…
Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the…
In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
We propose inflow and outflow boundary conditions for the compressible Navier-Stokes equations and prove that they allow a priori estimates of the entropy, mass and total energy. Furthermore, we demonstrate how to approximate these boundary…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We explore in this article the possibilities and limitations of the so-called energy method for analyzing the stability of finite difference approximations to the transport equation with extrapolation numerical boundary conditions at the…
This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the strong instability of standing waves associated with ground state solutions in the $L^2$-supercritical case.…
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A.…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…