Scientific Computing Group Seminars - Detail View

Speaker: N. C. Nguyen

Affiliation: Mechanical Engineering, MIT

Talk Title: Hybridized Discontinuous Galerkin Methods for Time-Dependent Convection-Diffusion Equations

Invited by: George Karniadakis

Time: May 23 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

We present implicit high-order hybridized discontinuous Galerkin (HDG) methods for the numerical solution of linear time-dependent convection-diffusion equations. In this method, the approximate solution and flux are expressed in an element-by-element fashion in terms of an approximate trace. This allows for elimination of both the approximate solution and flux to obtain a matrix equation in terms of the approximate trace only. The main disadvantages of a discontinuous Galerkin approximation --- a high number of globally coupled degrees of freedom for the same mesh and a low sparsity of the discrete system --- are thus eliminated to a significant extent. Moreover, the HDG method allows, in a single implementation, to use variable degrees and hanging nodes in different elements or subdomains of the computational domain. Finally, the HDG method appears attractive for the implicit time integration of the resulting system of ordinary differential equations. Numerical results for scalar and system cases are presented to assess the convergence and accuracy in both pure diffusion and pure convection limits.