The global element method for stationary advective problems

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Abstract
We extend the variation principle used in the global element method for self‐adjoint elliptic problems1, to problems containing advective terms. Used with the global element formalism, the extended principle yields a uniform framework for treating advective or boundary layer problems, with the attractive feature that the implicit treatment of interface conditions between elements yields an effective decoupling between ‘boundary layer’ and ‘interior’ parts of the solution. As a numerical example, we solve the one‐dimensional model problem of Christie and Mitchell3, obtaining high accuracy for Peclet numbers up to 106 with no sign of instability. These results suggest that, given a suitable choice of global elements, the decoupling is very effective in damping the oscillations found in standard finite difference or finite element treatment.

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