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.
翻译：在本文中,为动态 Euler-Bernoulli 光束方程式开发了一种基于能量的不连续的Galerkin 方法。 由此得出的方法是,根据对数字通量的简单、 网状独立选择, 节能或节能。 通过引入速度字段, 原始问题被转化成时间系统的第一阶。 在我们的配方中, 原始移位场和辅助速度字段的不连续的Galerkin 近似并不局限于同一空间。 特别是, 当速度字段的近似空间比移位场的近似空间低两级时, 一定的精确度可以以最小的自由度实现。 此外, 我们还在能源标准中设定误差估计值, 并展示数字实验中相应的最佳趋同性。
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