title:

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AP space discretizations of kinetic equations

abstract:

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We discuss the problem of space discretizations of kinetic equations

for small mean free path regimes. The model problem we consider is the

stationary linear transport equation used in neutron transport or

radiative transfer problems. We present the standard asymptotic

analysis that shows the existence of boundary layers in case of non

equilibrium boundary values. We show why standard upwind finite

difference methods fail to capture the solution when the boundary

layer is not resolved, and we explain the surprising result of Larsen

and Morel who were first to show that the linear discontinuous

Galerkin method works much better. We also discuss the recent work of

Guermond and Kanschat who have revisited the previous result in a

modern finite element framework. Finally, we give some examples in

other fields (like rarefied gas dynamics) where this work might be

very useful.