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The Continuous Galerkin Method Is Locally Conservative

✍ Scribed by Thomas J.R. Hughes; Gerald Engel; Luca Mazzei; Mats G. Larson

Book ID
102586856
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
198 KB
Volume
163
Category
Article
ISSN
0021-9991

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✦ Synopsis

We examine the conservation law structure of the continuous Galerkin method. We employ the scalar, advection-diffusion equation as a model problem for this purpose, but our results are quite general and apply to time-dependent, nonlinear systems as well. In addition to global conservation laws, we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements. These results are somewhat surprising and contradict the widely held opinion that the continuous Galerkin method is not locally conservative.

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