A posteriori analysis of the finite element discretization of some parabolic equations

نویسندگان

  • Amal Bergam
  • Christine Bernardi
  • Zoubida Mghazli
چکیده

We are interested in the discretization of parabolic equations, either linear or semilinear, by an implicit Euler scheme with respect to the time variable and finite elements with respect to the space variables. The main result of this paper consists of building error indicators with respect to both time and space approximations and proving their equivalence with the error, in order to work with adaptive time steps and finite element meshes. Résumé. Nous considérons la discrétisation d’équations paraboliques, soit linéaires soit semi-linéaires, par un schéma d’Euler implicite en temps et par éléments finis en espace. L’idée de cet article est de construire des indicateurs d’erreur liés à l’approximation en temps et en espace et de prouver leur équivalence avec l’erreur, dans le but de travailler avec des pas de temps adaptatifs et des maillages d’éléments finis adaptés à la solution.

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عنوان ژورنال:
  • Math. Comput.

دوره 74  شماره 

صفحات  -

تاریخ انتشار 2005