Discontinuous enrichment methods for computational fluid dynamics.

摘要

This dissertation develops and analyzes discontinuous enrichment methods (DEM) for the advection equation, the advection-diffusion equation and the Stokes problem. These methods fit into the class of hybrid finite elements, where continuity of the unknowns are enforced with Lagrange multipliers. The flexibility of employing globally discontinuous weighting functions allows us to choose fundamental solutions of the differential equation as shape functions (the enrichment functions), in analogy with the method of residual-free bubbles (RFB). The enrichment functions derived herein were crucial in capturing boundary-layers on advection-diffusion problems and stabilizing a low-order velocity-pressure pair for the Stokes problem. Numerical experiments contrast DEM with stabilized continuous and discontinuous Galerkin methods.