Discrete time Galerkin methods for a parabolic boundary value problem

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Single step discrete time Galerkin methods for the mixed initial-boundary value problem for the heat equation are studied. Two general theories leading to error estimates are developed. Among the examples analyzed in the application of these theories are methods in which the related quadratic form is required to be definite only on the subspace of approximating functions and two classes containing methods of arbitrary given order of accuracy, one requiring satisfaction of certain boundary conditions by the elements of the subspace, the other making no such requirements.


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Entrata in Redazione il 19 settembre 1972.

Sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462.

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Bramble, J.H., Thomée, V. Discrete time Galerkin methods for a parabolic boundary value problem. Annali di Matematica 101, 115–152 (1974) doi:10.1007/BF02417101

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  • Boundary Condition
  • Error Estimate
  • General Theory
  • Quadratic Form
  • Discrete Time