| Abstract: |
| This talk presents stabilized numerical simulations for the transport equation in a fluid while applying polygonal discretization. A convection-dominated problem explains convective and molecular transport along a given fluid velocity with a small diffusive effect, where classical numerical methods may yield spurious oscillations on numerical solutions and fail to provide accurate simulations. The edge-averaged finite element (EAFE) scheme is a stable discretization for the convection-dominated problem, and its stability is mathematically verified by the discrete maximum principle (DMP). We aim to generalize the edge-averaged stabilization to a polygonal discretization called the virtual element method. Hence, the edge-averaged virtual element (EAVE) methods produce stable and accurate numerical simulations on polygonal meshes and have less computational complexity than other stabilized schemes on polygons. We also show numerical experiments with numerical solutions with sharp boundary layers. |
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