相关论文: Generalized Galerkin Variational Integrators
Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here…
This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary…
We develop and analyze a local discontinuous Galerkin (LDG) method for solving integral fractional Laplacian problems on bounded Lipschitz domains. The method is based on a three-field mixed formulation involving the primal variable, its…
We present a discrete analog of the recently introduced Hamilton-Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
Consider a Urysohn integral equation $x - \mathcal{K} (x) = f$, where $f$ and the integral operator $\mathcal{K}$ with kernel of the type of Green's function are given. In the computation of approximate solutions of the given integral…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
We present a novel (high-order) hybridizable discontinuous Galerkin (HDG) scheme for the fluid-structure interaction (FSI) problem. The (moving domain) incompressible Navier-Stokes equations are discretized using a divergence-free HDG…
In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of…
A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the later is…
The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…
Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the coordinate singularities associated with local coordinate…
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than…
This article proposes and analyzes the generalized weak Galerkin ({\rm g}WG) finite element method for the second order elliptic problem. A generalized discrete weak gradient operator is introduced in the weak Galerkin framework so that the…
Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…
In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electrical circuit, one is faced with three special situations: 1. The system…
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev functions. By introducing numerical one-sided derivatives as…
In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koornwinder polynomials are introduced on the reference…