| Abstract: |
| This talk presents the development and analysis of nonconforming finite element methods, specifically the Morley and New-Zienkiewicz-type (NZT) elements, for the surface biharmonic problem and the stream function formulation of the surface Stokes problem. By employing appropriate stabilization techniques and geometric approximations, we address the challenges arising from the lack of $H^2$-conformity on discrete surfaces. Theoretical analysis establishes optimal convergence rates for the proposed schemes in various norms. Furthermore, we investigate the necessity and impact of stabilization terms through numerical experiments, providing insights into the robustness and efficiency of these nonconforming approximations for complex surface geometries. |
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