| Abstract: |
| The strict preservation of the conservation property is important in the design of numerical schemes for various model problems. I will firstly talk about why we would like to study low-degree strictly conservative finite element method for incompressible flows. Then I will talk about a nonstandard approach for designing finite element schemes for fluid computation, which can preserve strictly the divergence free condition for incompressible fluid flows. The schemes work on general triangulations with lower degree of polynomials than known results, and its superiority with respect to some existing schemes are partially illustrated with numerical experiments, including ones with boundary layers. The theoretical analysis depends on a careful application of Stokes complex. Both boundary value problems and eigenvalue problems will be mentioned, in case the time permits. |
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