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2002

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

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The dynamical behavior of the discontinuous Galerkin method and related difference schemes
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.
Donald J. Estep, Andrew M. Stuart
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where MOC
Authors Donald J. Estep, Andrew M. Stuart
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