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Numerische Mathematik

, Volume 75, Issue 3, pp 339–356 | Cite as

Galerkin and weighted Galerkin methods for a forward-backward heat equation

Summary.

Galerkin and weighted Galerkin methods are proposed for the numerical solution of parabolic partial differential equations where the diffusion coefficient takes different signs. The approach is based on a simultaneous discretization of space and time variables by using continuous finite element methods. Under some simple assumptions, error estimates and some numerical results for both Galerkin and weighted Galerkin methods are presented. Comparisons with the previous methods show that new methods not only can be used to solve a wider class of equations but also require less regularity for the solution and need fewer computations.

Mathematics Subject Classification (1991):65N30, 35K20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Hao Lu
    • 1
  1. 1.Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands; e-mail na.hlu@na-net.ornl.govNL

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