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Interior L estimates for finite element approximations of solutions of elliptic equations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 606)

Abstract

Let ∧⊂⊂ Ω⊂ \(\widetilde\Omega\) where \(\widetilde\Omega\) is the domain of definition of the solution of an elliptic equation. One assumes certain conditions of regularity on the equation and on the finite elements on Ω. Then one shows that the L2 (Ω) convergence of the approximate solution towards the exact solution implies the L (∧) convergence with the same order.

Keywords

  • Elliptic Equation
  • Dirichlet Form
  • Regular Element
  • Finite Element Approximation
  • Interior Estimate

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References

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© 1977 Springer-Verlag

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Descloux, J., Nassif, N. (1977). Interior L estimates for finite element approximations of solutions of elliptic equations. In: Galligani, I., Magenes, E. (eds) Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol 606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064456

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  • DOI: https://doi.org/10.1007/BFb0064456

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08432-7

  • Online ISBN: 978-3-540-37158-8

  • eBook Packages: Springer Book Archive