Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods

The present study is focused on the application of two families implicit time-integration schemes for general time-dependent balance laws convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely backward differentiation formulas (BDF) and diagonally Runge-Kutta (DIRK) methods. Special attention devoted to embedded DIRK methods, which allow incorporation time step size adaptation algorithms order keep computational effort as low possible. properties numerical solution, such its convergence, are investigated means suitably chosen test cases linear equation nonlinear system Navier-Stokes equations. For problems considered this work, methods prove be superior high-order BDF terms both stability accuracy.