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• W2904625862 abstract "This work is devoted to the high accuracy analysis of a discrete Stokes complex over rectangular meshes with a simple structure. The 0-form in the complex is a non $C^0$ nonconforming element space for biharmonic problems. This plate element contains only 12 degrees of freedom (DoFs) over a rectangular cell with a zeroth order weak continuity for the normal derivative, therefore only the lowest convergence order can be obtained by a standard consistency error analysis. Nevertheless, we prove that, if the rectangular mesh is uniform, an $O(h^2)$ convergence rate in discrete $H^2$-norm will be achieved. Moreover, based on a duality argument, it has an $O(h^3)$ convergence order in discrete $H^1$-norm if the solution region is convex. The 1-form and 2-form constitute a divergence-free pair for incompressible flow. We also show its higher accuracy than that derived from a usual error estimate under uniform partitions, which explains the phenomenon observed in our previous work. Numerical tests verify our theoretical results." @default.
• W2904625862 created "2018-12-22" @default.
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• W2904625862 date "2018-12-14" @default.
• W2904625862 modified "2023-10-05" @default.
• W2904625862 title "High accuracy analysis of a nonconforming discrete Stokes complex over rectangular meshes" @default.
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• W2904625862 hasPublicationYear "2018" @default.
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