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Higher order temporal finite element methods through mixed formalisms.

Jinkyu Kim1

  • 1School of Civil, Environmental and Architectural Engineering, Korea University, Anam-dong5-ga1, Seongbuk-goo, 136-713 South Korea.

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|September 12, 2014
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Summary
This summary is machine-generated.

New variational principles offer robust numerical methods for physics and mechanics problems. Algorithms derived from these principles demonstrate unconditional stability and accuracy for both damped and undamped systems.

Keywords:
Higher order methodsInitial value problemsMixed formulationTemporal finite element methodVariational formalism

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Area of Science:

  • Mathematical Physics
  • Mechanical Engineering
  • Numerical Analysis

Background:

  • Hamilton's principle and mixed convolved action principles offer variational formulations.
  • These principles are extended to create a weak variational formalism.
  • Investigating higher-order approximations is crucial for numerical methods.

Purpose of the Study:

  • To explore the potential of extended Hamilton's principle and mixed convolved action principle with higher-order approximations.
  • To validate and assess numerical algorithms derived from these principles.
  • To analyze the performance for classical single-degree-of-freedom dynamical systems.

Main Methods:

  • Development of numerical algorithms based on temporally higher order approximations.
  • Application of these algorithms to classical single-degree-of-freedom dynamical systems.
  • Analysis of stability and accuracy for both undamped and damped systems.

Main Results:

  • For undamped systems, all developed algorithms exhibit symplecticity and unconditional stability.
  • For damped systems, the algorithms demonstrate good accuracy and convergence properties.
  • The study validates the effectiveness of the proposed variational formulations.

Conclusions:

  • The extended variational principles provide a rigorous framework for initial boundary value problems.
  • Higher-order approximations enhance the performance of numerical algorithms.
  • The developed algorithms are suitable for analyzing damped and undamped dynamical systems.