UNSPECIFIED. (2002) The dynamical behavior of the discontinuous Galerkin method and related difference schemes. MATHEMATICS OF COMPUTATION, 71 (239). pp. 1075-1103. ISSN 0025-5718

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	MATHEMATICS OF COMPUTATION
Publisher:	AMER MATHEMATICAL SOC
ISSN:	0025-5718
Official Date:	2002
Dates:	Date Event 2002 UNSPECIFIED
Volume:	71
Number:	239
Number of Pages:	29
Page Range:	pp. 1075-1103
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/10980

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