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Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems

  • Mikhail M. Karchevsky EMAIL logo
Veröffentlicht/Copyright: 13. Juni 2019

Abstract

A class of Lagrangian mixed finite element methods is constructed for an approximate solution of a problem of nonlinear thin elastic shell theory, namely, the problem of finding critical points of the functional of potential energy according to the Budiansky–Sanders model. The proposed numerical method is based on the use of the second derivatives of the deflection as auxiliary variables. Sufficient conditions for the solvability of the corresponding discrete problem are obtained. Accuracy estimates for approximate solutions are established. Iterative methods for solving the corresponding systems of nonlinear equations are proposed and investigated.

MSC 2010: 65N30; 74K25

Award Identifier / Grant number: 18-41-160014

Award Identifier / Grant number: 19-08-01184

Funding statement: The research was supported by the Russian Foundation for Basic Research (projects 18-41-160014, 19-08-01184).

Acknowledgements

The author is grateful to the referees for the useful comments and helpful remarks.

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Received: 2019-01-28
Revised: 2019-03-25
Accepted: 2019-05-03
Published Online: 2019-06-13
Published in Print: 2020-10-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
  4. Special Issue Articles
  5. Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
  6. Weighted Estimates for Boundary Value Problems with Fractional Derivatives
  7. Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
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  9. Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
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  11. Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
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  13. Incomplete Iterative Implicit Schemes
  14. Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
  15. Regular Research Articles
  16. A General Superapproximation Result
  17. A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
  18. A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
  19. A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
  20. Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
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