The continuous Galerkin method is locally conservative
The authors examine the conservation law structure of the continuous Galerkin method for the scalar advection-diffusion equation, establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements. The results are quite general and apply to time-dependent, nonlinear systems as well and are somewhat surprising and contradict the widely held opinion that the continuous Galerkin method is not locally conservative.
scientific article; zbMATH DE number 1552737