The Scott-Vogelius finite elements revisited
arXiv:1705.0002076 citationsh-index: 32
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Provides a rigorous theoretical foundation for a widely used finite element method in computational fluid dynamics, but the result is incremental as it extends known stability to higher-order elements.
The paper proves that Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for velocity fields of degree k ≥ 4, resolving a long-standing theoretical gap.
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ($k \ge 4$).