An energy-based discontinuous Galerkin method for dynamic Euler-Bernoulli beam equations

09/15/2021
by   Lu Zhang, et al.
0

In this paper, an energy-based discontinuous Galerkin method for dynamic Euler-Bernoulli beam equations is developed. The resulting method is energy-dissipating or energy-conserving depending on the simple, mesh-independent choice of numerical fluxes. By introducing a velocity field, the original problem is transformed into a first-order in time system. In our formulation, the discontinuous Galerkin approximations for the original displacement field and the auxiliary velocity field are not restricted to be in the same space. In particular, a given accuracy can be achieved with the fewest degrees of freedom when the degree for the approximation space of the velocity field is two orders lower than the degree of approximation space for the displacement field. In addition, we establish the error estimates in an energy norm and demonstrate the corresponding optimal convergence in numerical experiments.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/25/2017

A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field

We introduce a hybridizable discontinuous Galerkin method for the incomp...
07/14/2020

Goal-oriented anisotropic hp-adaptive discontinuous Galerkin method for the Euler equations

We deal with the numerical solution of the compressible Euler equations ...
04/20/2020

Alias-free, matrix-free, and quadrature-free discontinuous Galerkin algorithms for (plasma) kinetic equations

Understanding fundamental kinetic processes is important for many proble...
05/04/2017

On the Necessity of Superparametric Geometry Representation for Discontinuous Galerkin Methods on Domains with Curved Boundaries

We provide numerical evidence demonstrating the necessity of employing a...
11/20/2021

Staggered Residual Distribution scheme for compressible flow

This paper is focused on the approximation of the Euler equation of comp...
06/29/2021

Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves

We present a new numerical approach for wave induced dynamic fracture. T...