相关论文: Hermite Methods for the Scalar Wave Equation
A type of discrete Boltzmann model for simulating shallow water flows is derived by using the Hermite expansion approach. Through analytical analysis, we study the impact of truncating distribution function and discretizing particle…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We study maximal estimates for the wave equation with orthonormal initial data. In dimension $d=3$, we establish optimal results with the sharp regularity exponent up to the endpoint. In higher dimensions $d \ge 4$ and also in $d=2$, we…
We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the…
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation,…
In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the…
We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we…
A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
We study the convergence rates of the semi-discrete (SD) method originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics,…
The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis…