An implicit HDG method for linear convection-diffusion with dual time stepping

This work presents, for the first time, a dual time stepping (DTS) approach to solve global system of equations that appears in hybridisable discontinuous Galerkin (HDG) formulation convection-diffusion problems. A proof existence and uniqueness steady state solution HDG problem with DTS is presented. The stability limit derived using von Neumann analysis, leading closed form expression critical step. An optimal choice step, producing maximum damping all frequencies, also derived. Steady transient problems are considered demonstrate performance proposed approach, particular emphasis on convection dominated Two simple approaches accelerate convergence three different marching compared.