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General variational principles applicable to the hybrid element method.

I Herrera1

  • 1Institute for Research in Applied Mathematics and Systems, National University of México, Apdo. Postal 20-726, México 20, D. F. Mexico.

Proceedings of the National Academy of Sciences of the United States of America
|July 1, 1977
PubMed
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This study introduces functional valued operators for abstract diffraction problems, developing variational principles. These principles are applied to free surface flows, potential theory, and elasticity.

Area of Science:

  • Mathematical physics
  • Applied mathematics
  • Continuum mechanics

Background:

  • Diffraction problems are often complex to model.
  • Existing formulations may lack generality.
  • Variational principles offer a powerful framework for physical theories.

Purpose of the Study:

  • To develop a general abstract formulation for diffraction problems using functional valued operators.
  • To establish and apply variational principles to this abstract framework.
  • To extend the application of these principles to fluid dynamics and solid mechanics.

Main Methods:

  • Utilizing functional valued operators for problem formulation.
  • Developing novel variational principles.
  • Applying the derived principles to specific physical systems.

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Main Results:

  • A generalized abstract formulation for diffraction problems.
  • Successful derivation of results in linearized free surface flow theory.
  • New applications in potential theory and elasticity.

Conclusions:

  • Functional valued operators provide a versatile tool for abstract diffraction modeling.
  • Variational principles are effectively applied to diverse physical phenomena.
  • The framework unifies approaches in fluid dynamics and elasticity.