C0 interior penalty methods for a dynamic nonlinear beam model

Jeongho Ahn, Seulip Lee, Eun Jae Park

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)685-700
Number of pages16
JournalApplied Mathematics and Computation
Volume339
DOIs
Publication statusPublished - 2018 Dec 15

Bibliographical note

Funding Information:
The research of EJP was supported in part by NRF , South Korea under grant nos. 2015R1A5A1009350 and 2016R1A2B4014358 .

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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