27 citations · 56 across the 16 of their papers we have counts for
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Cubic Lagrange elements satisfying exact incompressibility
Johnny Guzman, Ridgway Scott
We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the diver…
Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions
Johnny Guzman, Michael Neilan
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps…
Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes
Johnny Guzman, Alexandre Madureira, Marcus Sarkis +1
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, , surface without boundary on gener…
The Scott-Vogelius finite elements revisited
Johnny Guzman, Ridgway Scott
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ().