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A time-stepping method for Galerkin approximations for nonlinear parabolic equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 630)

Abstract

A modified backward difference time discretization is considered for Galerkin approximations to the solution of the nonlinear parabolic equation c(x, u)ut−▽·(a(x, u)▽u)=f(x, u). This procedure allows efficient use of such direct methods for solving linear algebraic equations as nested dissection. Optimal order error estimates and almost optimal order work requirements are derived.

Keywords

  • Linear Algebraic Equation
  • Optimal Order
  • Galerkin Approximation
  • Nonlinear Parabolic Equation
  • Parabolic Partial Differential Equation

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References

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© 1978 Springer-Verlag

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Douglas, J., Dupont, T., Percell, P. (1978). A time-stepping method for Galerkin approximations for nonlinear parabolic equations. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067697

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  • DOI: https://doi.org/10.1007/BFb0067697

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08538-6

  • Online ISBN: 978-3-540-35972-2

  • eBook Packages: Springer Book Archive