On commuting 𝑝-version projection-based interpolation on tetrahedra

Melenk, J.; Rojik, C.

doi:10.1090/mcom/3454

On commuting $p$-version projection-based interpolation on tetrahedra
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Math. Comp. 89 (2020), 45-87 Request permission

Abstract:

On the reference tetrahedron $\widehat K$, we define three projection-based interpolation operators on $H^2(\widehat K)$, ${\mathbf H}^1(\widehat K,\operatorname {\mathbf {curl}})$, and ${\mathbf H}^1(\widehat K,\operatorname {div})$. These operators are projections onto spaces of polynomials, they have the commuting diagram property, and they feature the optimal convergence rate as the polynomial degree increases in $H^{1-s}(\widehat K)$, $\widetilde {\mathbf {H}}^{-s}(\widehat K,\operatorname {\mathbf {curl}})$, and $\widetilde {\mathbf {H}}^{-s}(\widehat K,\operatorname {div})$ for $0 \leq s \leq 1$.

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