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Published July 2002 | public
Journal Article

The dynamical behavior of the discontinuous Galerkin method and related difference schemes

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.

Additional Information

© 2001 American Mathematical Society. Received by the editor May 24, 1999 and, in revised form, September 12, 2000. Published electronically: November 21, 2001. 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.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024