Related papers: Uniform stability estimates for the discrete Calde…
The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a…
We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…
We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…
The present paper, along with its sequel, establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute…
In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
This article establishes a discrete maximum principle (DMP) for the approximate solution of convection-diffusion-reaction problems obtained from the weak Galerkin finite element method on nonuniform rectangular partitions. The DMP analysis…
In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to…
This paper considers the robust ${\cal D}$-stability margin problem under polynomic structured real parametric uncertainty. Based on the work of De Gaston and Safonov (1988), we have developed techniques such as, a parallel frequency…
In our recent work [22], a family of high order asymptotic preserving (AP) methods, termed as IMEX-LDG methods, are designed to solve some linear kinetic transport equations, including the one-group transport equation in slab geometry and…
We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
The classical $S_n$ equations of Carlson and Lee have been a mainstay in multi-dimensional radiation transport calculations. In this paper, an alternative to the $S_n$ equations, the "Lagrange Discrete Ordinate" (LDO) equations are derived.…
The method and the formula of variation of constants for ordinary differential equations (ODEs) is a fundamental tool to analyze the dynamics of an ODE near an equilibrium. It is natural to expect that such a formula works for delay…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…