An edgewise iterative scheme for the discontinuous Galerkin method with Lagrange multiplier for Poisson’s equation

Abstract

An edgewise iterative scheme is developed for large systems of equations resulting from the discretization by the discontinuous Galerkin method with Lagrange multiplier for the Poisson’s equation. The solution is computed element by element. Lagrange multiplier is edgewise updated, which is given as the average of the Robin type information on the elements sharing the edge. Analysis of the convergence of the scheme is given with the discrete maximum norm over all the edges. Several numerical experiments are presented.