C0 interior penalty methods for a dynamic nonlinear beam model

Jeongho Ahn, Seulip Lee and Eun-Jae Park

Applied Mathematics and Computation, 2018, vol. 339, issue C, 685-700

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.

Keywords: C0 interior penalty method; Discontinuous Galerkin; Finite element methods; Gao Beams; Pseudomonotone (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:685-700

DOI: 10.1016/j.amc.2018.07.043

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