The continuous Galerkin method is locally conservative

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-dependen t, nonlinear systems as well. In addition to global conservation laws, we e stablish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements. These results are somew hat surprising and contradict the widely held opinion that the continuous G alerkin method is not locally conservative. (C) 2000 Academic Press.