相关论文: Antisymmetry, pseudospectral methods, and conserva…

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…

We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry:…

We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…

We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic discretisation based on this new formulation is exemplified by…

We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…

We present a method to obtain symmetries for second-order systems of ordinary difference equations and how to use them to reduce the order. We also introduce a technique of finding conservation laws for such systems.

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…

In this work, we introduce new second-order schemes for one- and two-dimensional hyperbolic systems of conservation laws. Following an approach recently proposed in [{\sc R. Abgrall}, Commun. Appl. Math. Comput., 5 (2023), pp. 370--402], we…

We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg-de Vries…

Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…

We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…

We consider a prototypical parabolic SPDE with finite-dimensional multiplicative noise, which, subject to a nonnegative initial datum, has a unique nonnegative solution. Inspired by well-established techniques in the deterministic case, we…

We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…

In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…

In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…

A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical…

For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…