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

@article{Zhang2021AnED, title={An energy-based discontinuous Galerkin method for dynamic Euler-Bernoulli beam equations}, author={Lu Zhang}, journal={ArXiv}, year={2021}, volume={abs/2109.07033} }

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… Expand

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This paper develops the paradigm of the local discontinuous Galerkin method by introducing the second-order spatial derivative as an auxiliary variable instead of the conventional first-order derivative, and derives optimal L-error estimates of the scheme that measure both the solution and the auxiliary variable. Expand

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