The dynamical behavior of the discontinuous Galerkin method and related difference schemes
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- by Donald J. Estep and Andrew M. Stuart PDF
- Math. Comp. 71 (2002), 1075-1103 Request permission
Abstract:
We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee that the continuous problem defines a dissipative dynamical system. We show that, under certain conditions, the discontinuous Galerkin approximation also defines a dissipative dynamical system and we study the approximation properties of the associated discrete dynamical system. We also study the behavior of difference schemes obtained by applying a quadrature formula to the integrals defining the discontinuous Galerkin approximation and construct two kinds of discrete finite element approximations that share the dissipativity properties of the original method.References
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Additional Information
- Donald J. Estep
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- Email: estep@math.colostate.edu
- Andrew M. Stuart
- Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
- Email: stuart@maths.warwick.ac.uk
- Received by editor(s): May 24, 1999
- Received by editor(s) in revised form: September 12, 2000
- Published electronically: November 21, 2001
- Additional Notes: The research of the first author was partially supported by the National Science Foundation, DMS 9805748.
The research of the second author was partially supported by the Office of Naval Research under grant No. N00014-92-J-1876 and by the National Science Foundation under grant No. DMS-9201727. - © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 1075-1103
- MSC (2000): Primary 65L07
- DOI: https://doi.org/10.1090/S0025-5718-01-01364-3
- MathSciNet review: 1898746