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A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation

✍ Scribed by Peterson, Todd E.

Book ID
118187392
Publisher
Society for Industrial and Applied Mathematics
Year
1991
Tongue
English
Weight
631 KB
Volume
28
Category
Article
ISSN
0036-1429

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✦ Synopsis

A numerical example is presented which shows that the known L error estimate ]tu-uhl] =< Chk+/21] u k+ for the discontinuous Galerkin method cannot be improved within the class of quasi-uniform meshes, not even for smooth exact solutions u.

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## a b s t r a c t We present a new discontinuous Galerkin method for solving the second-order wave equation using the standard continuous finite element method in space and a discontinuous method in time directly applied to second-order ode systems. We prove several optimal a priori error estimate