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C0 interior penalty methods for a dynamic nonlinear beam model

Author

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  • Ahn, Jeongho
  • Lee, Seulip
  • Park, Eun-Jae

Abstract

In this work, we aim to develop efficient numerical schemes for a nonlinear fourth-order partial differential equation arising from the so-called dynamic Gao beam model. We use C0 interior penalty finite element methods over the spatial domain to set up the semi-discrete formulations. Convergence results for the semi-discrete case are shown, based on a truncated variational formulation and its equivalent abstract formulations. We combine time discretizations to derive fully discrete numerical formulations. Newton’s method is applied to compute one time step numerical solutions of a nonlinear system. Two numerical examples are provided: one supports our theoretical results and the other presents a buckling state of the Gao beams.

Suggested Citation

  • Ahn, Jeongho & Lee, Seulip & Park, Eun-Jae, 2018. "C0 interior penalty methods for a dynamic nonlinear beam model," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 685-700.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:685-700
    DOI: 10.1016/j.amc.2018.07.043
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    Cited by:

    1. Ahn, Jeongho & Rail, Zachary, 2021. "A rod-beam system with dynamic contact and thermal exchange condition," Applied Mathematics and Computation, Elsevier, vol. 388(C).

    More about this item

    Keywords

    C0 interior penalty method; Discontinuous Galerkin; Finite element methods; Gao Beams; Pseudomonotone;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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