An interpretation of the galerkin method as the realization of a discrete hodge operator

摘要

In this paper an interpretation of the Galerkin method as the realization of a discrete Hodge operator in the Whitney complex is presented. A discrete Hodge operator is a metric-dependent linear operator mapping the degrees of freedom from the primal side to the dual side of the Whitney complex. A Hodge operator enables the separation of topology and metrics from each other in finite element approaches.