Scientific Computing Group Seminars - Detail View

Speaker: J. Yan

Affiliation: Iowa State University

Talk Title: The Direct Discontinuous Galerkin (DDG) Methods for Diffusion with interface correction

Invited by: Chi-Wang Shu

Time: March 13 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

In (1) we proposed a general numerical flux formula for the solution derivative u_x, and developed the so-called direct discontinuous Gallerkin (DDG) method. The DDG method has the drawback of obtaining its optimal accuracy when k is even for p^k polynomials. In this talk, we introduce a refined DDG method such that optimal (k+1)'th order of accuracy is obtained for any p^k polynomial approximations. Two types of admissible numerical fluxes are studied. Admissibility and stability are discussed, and then the DDG method with interface correction is extended to nonlinear convection diffusion equations. Two dimensional extension is carried out also. A series of numerical examples are presented to demonstrate the high order accuracy and the capacity of the method. Reference: (1)Liu, H. and Yan, J.,The direct discontinuous Galerkin method for diffusion problems, SIAM J. Numer. Anal 47, #1, January 16 2009, available online.