In numerical analysis, we focus on developing and analysing advanced discretization schemes, including their stability and convergence properties, using, e.g., tools from functional analysis.

YAN XU, CHI-WANG SHU, OPTIMAL ERROR ESTIMATES OF THE SEMIDISCRETE LOCAL DISCONTINUOUS GALERKIN METHODS FOR HIGH ORDER WAVE EQUATIONS, SIAM Journal on Numerical Analysis, Vol. 50, No. 1 (2012), pp.

In this paper we show that whenever the discrete-ordinate method has the correct diffusion limit, both in the interior and at the boundaries, its solutions converge to the solution of the transport ...