# C0 interior penalty methods for a dynamic nonlinear beam model

Jeongho Ahn, Seulip Lee, Eun-Jae Park

Research output: Contribution to journalArticle

### 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 language English 685-700 16 Applied Mathematics and Computation 339 https://doi.org/10.1016/j.amc.2018.07.043 Published - 2018 Dec 15

### Fingerprint

Interior Methods
Interior Penalty
Penalty Method
Newton-Raphson method
Nonlinear Dynamics
Partial differential equations
Buckling
Nonlinear systems
Finite element method
Formulation
Time Discretization
Variational Formulation
Newton Methods
Convergence Results
Numerical Scheme
Fourth Order
Partial differential equation
Nonlinear Systems
Finite Element Method
Numerical Solution

### All Science Journal Classification (ASJC) codes

• Computational Mathematics
• Applied Mathematics

### Cite this

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title = "C0 interior penalty methods for a dynamic nonlinear beam model",
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.",
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C0 interior penalty methods for a dynamic nonlinear beam model. / Ahn, Jeongho; Lee, Seulip; Park, Eun-Jae.

In: Applied Mathematics and Computation, Vol. 339, 15.12.2018, p. 685-700.

Research output: Contribution to journalArticle

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T1 - C0 interior penalty methods for a dynamic nonlinear beam model

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AU - Lee, Seulip

AU - Park, Eun-Jae

PY - 2018/12/15

Y1 - 2018/12/15

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AB - 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.

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