A hybrid discontinuous Galerkin method for transport equations on networks
Submission Status: | in press |
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- We discuss the mathematical modeling and numerical discretization of
5 transport problems on one-dimensional networks. Suitable coupling conditions are
derived that guarantee conservation of mass across network junctions and dissipation
of a mathematical energy which allows us to prove existence of unique solutions.
We then consider the space discretization by a hybrid discontinuous Galerkin
method which provides a suitable upwind mechanism to handle the transport prob10
lem and allows to incorporate the coupling conditions in a natural manner. In addition,
the method inherits mass conservation and stability of the continuous problem.
Order optimal convergence rates are established and illustrated by numerical tests.