Numerical Analysis of a Locally Projected Discontinuous Galerkin Method for Elliptic Problems

Abstract

In this paper we study a new discontinuous Galerkin method which uses a computational structure compatible with conforming finite element methods, reducing considerably the number of degrees-of-freedom. The Locally Discontinuous but Globally Continuous Galerkin method starts with a discontinuous finite element space and constructs a continuous representation for it by means of local projections. The used technique is similar to that employed in hybridizable methods, and discontinuous solution is recovered by solving local element-wise problems. We present the numerical analysis of the method and numerical results to confirm the predicted convergence rates. Moreover, numerical experiments are conducted in order to evaluate the better performance of this formulation when compared to the continuous or discontinuous Galerkin formulations.