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.

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HAIJIN WANG, CHI-WANG SHU, QIANG ZHANG, STABILITY AND ERROR ESTIMATES OF LOCAL DISCONTINUOUS GALERKIN METHODS WITH IMPLICIT-EXPLICIT TIME-MARCHING FOR ADVECTION-DIFFUSION PROBLEMS, SIAM Journal on ...

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 ...