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Error estimates for spatially discrete approximations of semilinear parabolic equations with initial data of low regularity

Authors: M. Crouzeix, V. Thomée and L. B. Wahlbin
Journal: Math. Comp. 53 (1989), 25-41
MSC: Primary 65N10
MathSciNet review: 970700
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Abstract: Semidiscrete finite element methods for a semilinear parabolic equation in $ {R^d}$, $ d \leq 3$, were considered by Johnson, Larsson, Thomée, and Wahlbin. With h the discretization parameter, it was proved that, for compatible and bounded initial data in $ {H^\alpha }$, the convergence rate is essentially $ O({h^{2 + \alpha }})$ for t positive, and for $ \alpha = 0$ this was seen to be best possible. Here we shall show that for $ 0 \leq \alpha < 2$ the convergence rate is, in fact, essentially $ O({h^{2 + 2\alpha }})$, which is sharp.

References [Enhancements On Off] (What's this?)

  • [1] H.-P. Helfrich "Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data," Numer. Math., v. 51, 1987, pp. 559-569. MR 910865 (88j:65130)
  • [2] C. Johnson, S. Larsson, V. Thomée & L. B. Wahlbin, "Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data," Math. Comp., v. 49, 1987, pp. 331-357. MR 906175 (88k:65100)
  • [3] J. Moser, "A rapidly convergent iteration method and nonlinear partial differential equations. I," Ann. Scuola Norm. Sup. Pisa, v. 20, 1966, pp. 265-315. MR 0199523 (33:7667)
  • [4] V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer, New York, 1984. MR 744045 (86k:65006)

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Article copyright: © Copyright 1989 American Mathematical Society

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